{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cZGDvdVGplrP"
      },
      "source": [
        "# DDPM: Training a Diffusion Model on MNIST\n",
        "\n",
        "This notebook implements a DDPM (Denoising Diffusion Probabilistic Model)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "NR35_kZFplrQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b67cbe2b-4f0b-4f06-de20-979ebf26dcd9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Using device: cuda\n",
            "GPU: NVIDIA A100-SXM4-40GB\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "from torch.utils.data import DataLoader\n",
        "from torchvision import datasets, transforms\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "from tqdm import tqdm\n",
        "\n",
        "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
        "print(f\"Using device: {device}\")\n",
        "if torch.cuda.is_available():\n",
        "    print(f\"GPU: {torch.cuda.get_device_name(0)}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UmtmIGZmplrR"
      },
      "source": [
        "## 1. Noise Schedule\n",
        "\n",
        "We use a linear schedule for $\\beta_t$ from $\\beta_1 = 0.0001$ to $\\beta_T = 0.02$.\n",
        "\n",
        "Recall:\n",
        "- $\\alpha_t = 1 - \\beta_t$\n",
        "- $\\bar{\\alpha}_t = \\prod_{i=1}^{t} \\alpha_i$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "xcWA5wJrplrR"
      },
      "outputs": [],
      "source": [
        "class NoiseSchedule:\n",
        "    def __init__(self, T=1000, beta_1=0.0001, beta_T=0.02, device='cpu'):\n",
        "        self.T = T\n",
        "        self.device = device\n",
        "\n",
        "        self.beta = torch.linspace(beta_1, beta_T, T, device=device)\n",
        "        self.alpha = 1.0 - self.beta\n",
        "        self.alpha_bar = torch.cumprod(self.alpha, dim=0)\n",
        "        self.alpha_bar_prev = F.pad(self.alpha_bar[:-1], (1, 0), value=1.0)\n",
        "\n",
        "        # For sampling\n",
        "        self.sigma2 = (1 - self.alpha) * (1 - self.alpha_bar_prev) / (1 - self.alpha_bar)\n",
        "        self.sigma = torch.sqrt(self.sigma2)\n",
        "\n",
        "T = 1000\n",
        "schedule = NoiseSchedule(T=T, device=device)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Plot the schedule\n",
        "fig, axes = plt.subplots(1, 3, figsize=(12, 3))\n",
        "t = np.arange(1, T+1)\n",
        "axes[0].plot(t, schedule.beta.cpu().numpy())\n",
        "axes[0].set_xlabel('t'); axes[0].set_ylabel(r'$\\beta_t$'); axes[0].set_title(r'$\\beta_t$')\n",
        "axes[1].plot(t, schedule.alpha.cpu().numpy())\n",
        "axes[1].set_xlabel('t'); axes[1].set_ylabel(r'$\\alpha_t$'); axes[1].set_title(r'$\\alpha_t = 1 - \\beta_t$')\n",
        "axes[2].plot(t, schedule.alpha_bar.cpu().numpy())\n",
        "axes[2].set_xlabel('t'); axes[2].set_ylabel(r'$\\bar{\\alpha}_t$'); axes[2].set_title(r'$\\bar{\\alpha}_t$')\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 152
        },
        "id": "VLh82Fp4qCBo",
        "outputId": "f4251680-f004-4085-ae49-57a3e6dab163"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x300 with 3 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8TA8L-faplrS"
      },
      "source": [
        "## 2. Forward Process\n",
        "\n",
        "The forward process adds noise to data:\n",
        "$$x_t = \\sqrt{\\bar{\\alpha}_t} \\, x_0 + \\sqrt{1 - \\bar{\\alpha}_t} \\, \\varepsilon, \\quad \\varepsilon \\sim N(0, I)$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "96exHYa5plrS"
      },
      "outputs": [],
      "source": [
        "def forward_process(x_0, t, schedule):\n",
        "    \"\"\"x_t = sqrt(alpha_bar_t) * x_0 + sqrt(1 - alpha_bar_t) * epsilon\"\"\"\n",
        "    epsilon = torch.randn_like(x_0)\n",
        "    alpha_bar_t = schedule.alpha_bar[t].view(-1, 1, 1, 1)\n",
        "    x_t = torch.sqrt(alpha_bar_t) * x_0 + torch.sqrt(1 - alpha_bar_t) * epsilon\n",
        "    return x_t, epsilon"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KxQxvBBGplrS"
      },
      "source": [
        "## 3. Model Architecture\n",
        "\n",
        "We use a U-Net with time embedding. The model predicts $\\hat{\\varepsilon}_\\theta(x_t, t)$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "ron26NKfplrS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "15b86c31-b8f4-439a-b84b-8379dcc68c86"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Input: torch.Size([4, 1, 28, 28]), Output: torch.Size([4, 1, 28, 28])\n",
            "Parameters: 16,775,937\n"
          ]
        }
      ],
      "source": [
        "class SinusoidalPositionEmbeddings(nn.Module):\n",
        "    def __init__(self, dim):\n",
        "        super().__init__()\n",
        "        self.dim = dim\n",
        "\n",
        "    def forward(self, t):\n",
        "        device = t.device\n",
        "        half_dim = self.dim // 2\n",
        "        emb = np.log(10000) / (half_dim - 1)\n",
        "        emb = torch.exp(torch.arange(half_dim, device=device) * -emb)\n",
        "        emb = t[:, None] * emb[None, :]\n",
        "        emb = torch.cat((emb.sin(), emb.cos()), dim=-1)\n",
        "        return emb\n",
        "\n",
        "\n",
        "class ResidualBlock(nn.Module):\n",
        "    \"\"\"Residual block with time embedding.\"\"\"\n",
        "    def __init__(self, in_ch, out_ch, time_emb_dim, dropout=0.1):\n",
        "        super().__init__()\n",
        "        self.conv1 = nn.Conv2d(in_ch, out_ch, 3, padding=1)\n",
        "        self.conv2 = nn.Conv2d(out_ch, out_ch, 3, padding=1)\n",
        "        self.norm1 = nn.GroupNorm(8, in_ch)\n",
        "        self.norm2 = nn.GroupNorm(8, out_ch)\n",
        "        self.time_mlp = nn.Linear(time_emb_dim, out_ch)\n",
        "        self.dropout = nn.Dropout(dropout)\n",
        "\n",
        "        # Skip connection if channels change\n",
        "        if in_ch != out_ch:\n",
        "            self.skip = nn.Conv2d(in_ch, out_ch, 1)\n",
        "        else:\n",
        "            self.skip = nn.Identity()\n",
        "\n",
        "    def forward(self, x, t_emb):\n",
        "        h = F.silu(self.norm1(x))\n",
        "        h = self.conv1(h)\n",
        "\n",
        "        # Add time embedding\n",
        "        h = h + self.time_mlp(F.silu(t_emb))[:, :, None, None]\n",
        "\n",
        "        h = F.silu(self.norm2(h))\n",
        "        h = self.dropout(h)\n",
        "        h = self.conv2(h)\n",
        "\n",
        "        return h + self.skip(x)\n",
        "\n",
        "\n",
        "class AttentionBlock(nn.Module):\n",
        "    \"\"\"Self-attention block.\"\"\"\n",
        "    def __init__(self, channels):\n",
        "        super().__init__()\n",
        "        self.norm = nn.GroupNorm(8, channels)\n",
        "        self.q = nn.Conv2d(channels, channels, 1)\n",
        "        self.k = nn.Conv2d(channels, channels, 1)\n",
        "        self.v = nn.Conv2d(channels, channels, 1)\n",
        "        self.proj = nn.Conv2d(channels, channels, 1)\n",
        "        self.scale = channels ** -0.5\n",
        "\n",
        "    def forward(self, x):\n",
        "        b, c, h, w = x.shape\n",
        "\n",
        "        x_norm = self.norm(x)\n",
        "        q = self.q(x_norm).view(b, c, -1)  # (b, c, h*w)\n",
        "        k = self.k(x_norm).view(b, c, -1)\n",
        "        v = self.v(x_norm).view(b, c, -1)\n",
        "\n",
        "        # Attention: softmax(Q^T K / sqrt(d)) V^T\n",
        "        attn = torch.bmm(q.transpose(1, 2), k) * self.scale  # (b, h*w, h*w)\n",
        "        attn = F.softmax(attn, dim=-1)\n",
        "\n",
        "        out = torch.bmm(v, attn.transpose(1, 2))  # (b, c, h*w)\n",
        "        out = out.view(b, c, h, w)\n",
        "\n",
        "        return x + self.proj(out)\n",
        "\n",
        "\n",
        "class Downsample(nn.Module):\n",
        "    def __init__(self, channels):\n",
        "        super().__init__()\n",
        "        self.conv = nn.Conv2d(channels, channels, 3, stride=2, padding=1)\n",
        "\n",
        "    def forward(self, x):\n",
        "        return self.conv(x)\n",
        "\n",
        "\n",
        "class Upsample(nn.Module):\n",
        "    def __init__(self, channels):\n",
        "        super().__init__()\n",
        "        self.conv = nn.Conv2d(channels, channels, 3, padding=1)\n",
        "\n",
        "    def forward(self, x):\n",
        "        x = F.interpolate(x, scale_factor=2, mode='nearest')\n",
        "        return self.conv(x)\n",
        "\n",
        "\n",
        "class UNet(nn.Module):\n",
        "    \"\"\"\n",
        "    U-Net for MNIST with ~5M parameters.\n",
        "\n",
        "    Architecture:\n",
        "    - Encoder: 28→14→7 with channels 128→256→256\n",
        "    - Attention at 7×7\n",
        "    - 2 residual blocks per resolution\n",
        "    \"\"\"\n",
        "    def __init__(self, in_channels=1, base_channels=128, time_emb_dim=256):\n",
        "        super().__init__()\n",
        "\n",
        "        # Time embedding MLP\n",
        "        self.time_mlp = nn.Sequential(\n",
        "            SinusoidalPositionEmbeddings(base_channels),\n",
        "            nn.Linear(base_channels, time_emb_dim),\n",
        "            nn.SiLU(),\n",
        "            nn.Linear(time_emb_dim, time_emb_dim),\n",
        "        )\n",
        "\n",
        "        # Initial conv\n",
        "        self.init_conv = nn.Conv2d(in_channels, base_channels, 3, padding=1)\n",
        "\n",
        "        # Encoder\n",
        "        # Level 1: 28×28, 128 channels\n",
        "        self.down1_block1 = ResidualBlock(base_channels, base_channels, time_emb_dim)\n",
        "        self.down1_block2 = ResidualBlock(base_channels, base_channels, time_emb_dim)\n",
        "        self.down1 = Downsample(base_channels)\n",
        "\n",
        "        # Level 2: 14×14, 256 channels\n",
        "        self.down2_block1 = ResidualBlock(base_channels, base_channels * 2, time_emb_dim)\n",
        "        self.down2_block2 = ResidualBlock(base_channels * 2, base_channels * 2, time_emb_dim)\n",
        "        self.down2 = Downsample(base_channels * 2)\n",
        "\n",
        "        # Level 3: 7×7, 256 channels + attention\n",
        "        self.down3_block1 = ResidualBlock(base_channels * 2, base_channels * 2, time_emb_dim)\n",
        "        self.down3_attn = AttentionBlock(base_channels * 2)\n",
        "        self.down3_block2 = ResidualBlock(base_channels * 2, base_channels * 2, time_emb_dim)\n",
        "\n",
        "        # Bottleneck: 7×7\n",
        "        self.mid_block1 = ResidualBlock(base_channels * 2, base_channels * 2, time_emb_dim)\n",
        "        self.mid_attn = AttentionBlock(base_channels * 2)\n",
        "        self.mid_block2 = ResidualBlock(base_channels * 2, base_channels * 2, time_emb_dim)\n",
        "\n",
        "        # Decoder\n",
        "        # Level 3: 7×7 (with skip from down3)\n",
        "        self.up3_block1 = ResidualBlock(base_channels * 4, base_channels * 2, time_emb_dim)\n",
        "        self.up3_attn = AttentionBlock(base_channels * 2)\n",
        "        self.up3_block2 = ResidualBlock(base_channels * 2, base_channels * 2, time_emb_dim)\n",
        "        self.up3 = Upsample(base_channels * 2)\n",
        "\n",
        "        # Level 2: 14×14 (with skip from down2)\n",
        "        self.up2_block1 = ResidualBlock(base_channels * 4, base_channels * 2, time_emb_dim)\n",
        "        self.up2_block2 = ResidualBlock(base_channels * 2, base_channels, time_emb_dim)\n",
        "        self.up2 = Upsample(base_channels)\n",
        "\n",
        "        # Level 1: 28×28 (with skip from down1)\n",
        "        self.up1_block1 = ResidualBlock(base_channels * 2, base_channels, time_emb_dim)\n",
        "        self.up1_block2 = ResidualBlock(base_channels, base_channels, time_emb_dim)\n",
        "\n",
        "        # Output\n",
        "        self.out_norm = nn.GroupNorm(8, base_channels)\n",
        "        self.out_conv = nn.Conv2d(base_channels, in_channels, 3, padding=1)\n",
        "\n",
        "    def forward(self, x, t):\n",
        "        # Time embedding\n",
        "        t_emb = self.time_mlp(t)\n",
        "\n",
        "        # Initial conv\n",
        "        x = self.init_conv(x)\n",
        "\n",
        "        # Encoder\n",
        "        d1 = self.down1_block1(x, t_emb)\n",
        "        d1 = self.down1_block2(d1, t_emb)  # 28×28, 128ch\n",
        "\n",
        "        d2 = self.down1(d1)\n",
        "        d2 = self.down2_block1(d2, t_emb)\n",
        "        d2 = self.down2_block2(d2, t_emb)  # 14×14, 256ch\n",
        "\n",
        "        d3 = self.down2(d2)\n",
        "        d3 = self.down3_block1(d3, t_emb)\n",
        "        d3 = self.down3_attn(d3)\n",
        "        d3 = self.down3_block2(d3, t_emb)  # 7×7, 256ch\n",
        "\n",
        "        # Bottleneck\n",
        "        h = self.mid_block1(d3, t_emb)\n",
        "        h = self.mid_attn(h)\n",
        "        h = self.mid_block2(h, t_emb)  # 7×7, 256ch\n",
        "\n",
        "        # Decoder\n",
        "        h = torch.cat([h, d3], dim=1)  # 7×7, 512ch\n",
        "        h = self.up3_block1(h, t_emb)\n",
        "        h = self.up3_attn(h)\n",
        "        h = self.up3_block2(h, t_emb)\n",
        "        h = self.up3(h)  # 14×14, 256ch\n",
        "\n",
        "        h = torch.cat([h, d2], dim=1)  # 14×14, 512ch\n",
        "        h = self.up2_block1(h, t_emb)\n",
        "        h = self.up2_block2(h, t_emb)\n",
        "        h = self.up2(h)  # 28×28, 128ch\n",
        "\n",
        "        h = torch.cat([h, d1], dim=1)  # 28×28, 256ch\n",
        "        h = self.up1_block1(h, t_emb)\n",
        "        h = self.up1_block2(h, t_emb)  # 28×28, 128ch\n",
        "\n",
        "        # Output\n",
        "        h = F.silu(self.out_norm(h))\n",
        "        return self.out_conv(h)\n",
        "\n",
        "\n",
        "# Test\n",
        "model = UNet().to(device)\n",
        "x_test = torch.randn(4, 1, 28, 28, device=device)\n",
        "t_test = torch.randint(0, T, (4,), device=device).float()\n",
        "out = model(x_test, t_test)\n",
        "print(f\"Input: {x_test.shape}, Output: {out.shape}\")\n",
        "print(f\"Parameters: {sum(p.numel() for p in model.parameters()):,}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jc0Qn2IwplrS"
      },
      "source": [
        "## 4. Data"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "hwUjGW8vplrT",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d59370c0-5582-4ce7-ac04-4b5a0fb0e80f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Dataset: 60000 images\n",
            "Batches per epoch: 469\n"
          ]
        }
      ],
      "source": [
        "transform = transforms.Compose([\n",
        "    transforms.ToTensor(),\n",
        "    transforms.Normalize((0.5,), (0.5,))  # Scale to [-1, 1]\n",
        "])\n",
        "\n",
        "train_dataset = datasets.MNIST(root='./data', train=True, download=True, transform=transform)\n",
        "train_loader = DataLoader(train_dataset, batch_size=128, shuffle=True, num_workers=2, pin_memory=True)\n",
        "\n",
        "print(f\"Dataset: {len(train_dataset)} images\")\n",
        "print(f\"Batches per epoch: {len(train_loader)}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_4yFXFmsplrT"
      },
      "source": [
        "## 5. Training\n",
        "\n",
        "Using the simplified $\\varepsilon$-prediction objective:\n",
        "$$L_{\\mathrm{simple}}(\\theta) = \\mathbb{E}_{t, x_0, \\varepsilon}\\left[\\|\\varepsilon - \\hat{\\varepsilon}_\\theta(x_t, t)\\|^2\\right]$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "H4YOTGP7plrT"
      },
      "outputs": [],
      "source": [
        "def train_step(model, x_0, schedule, optimizer):\n",
        "    optimizer.zero_grad()\n",
        "\n",
        "    batch_size = x_0.shape[0]\n",
        "    t = torch.randint(0, schedule.T, (batch_size,), device=x_0.device)\n",
        "\n",
        "    x_t, epsilon = forward_process(x_0, t, schedule)\n",
        "    epsilon_pred = model(x_t, t.float())\n",
        "\n",
        "    loss = F.mse_loss(epsilon_pred, epsilon)\n",
        "\n",
        "    loss.backward()\n",
        "    # Gradient clipping for stability\n",
        "    torch.nn.utils.clip_grad_norm_(model.parameters(), 1.0)\n",
        "    optimizer.step()\n",
        "\n",
        "    return loss.item()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "id": "7VAhuTiyplrT",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "cf762821-0820-4537-fdac-efd5c8a2c381"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Epoch 1/15: 100%|██████████| 469/469 [00:27<00:00, 16.98it/s, loss=0.0385]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/15, Loss: 0.0575, LR: 0.000198\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Epoch 2/15: 100%|██████████| 469/469 [00:27<00:00, 17.21it/s, loss=0.0323]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 2/15, Loss: 0.0289, LR: 0.000191\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Epoch 3/15: 100%|██████████| 469/469 [00:27<00:00, 17.01it/s, loss=0.0269]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 3/15, Loss: 0.0263, LR: 0.000181\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Epoch 4/15: 100%|██████████| 469/469 [00:27<00:00, 17.26it/s, loss=0.0259]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 4/15, Loss: 0.0251, LR: 0.000167\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Epoch 5/15: 100%|██████████| 469/469 [00:27<00:00, 17.23it/s, loss=0.0303]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 5/15, Loss: 0.0246, LR: 0.000150\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Epoch 6/15: 100%|██████████| 469/469 [00:27<00:00, 17.21it/s, loss=0.0186]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 6/15, Loss: 0.0239, LR: 0.000131\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Epoch 7/15: 100%|██████████| 469/469 [00:27<00:00, 17.07it/s, loss=0.0249]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 7/15, Loss: 0.0233, LR: 0.000110\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Epoch 8/15: 100%|██████████| 469/469 [00:27<00:00, 17.16it/s, loss=0.0244]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 8/15, Loss: 0.0232, LR: 0.000090\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Epoch 9/15: 100%|██████████| 469/469 [00:27<00:00, 17.21it/s, loss=0.0193]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 9/15, Loss: 0.0226, LR: 0.000069\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Epoch 10/15: 100%|██████████| 469/469 [00:27<00:00, 17.16it/s, loss=0.0222]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 10/15, Loss: 0.0226, LR: 0.000050\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Epoch 11/15: 100%|██████████| 469/469 [00:27<00:00, 17.11it/s, loss=0.0230]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 11/15, Loss: 0.0221, LR: 0.000033\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Epoch 12/15: 100%|██████████| 469/469 [00:27<00:00, 17.18it/s, loss=0.0245]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 12/15, Loss: 0.0220, LR: 0.000019\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Epoch 13/15: 100%|██████████| 469/469 [00:27<00:00, 17.19it/s, loss=0.0226]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 13/15, Loss: 0.0218, LR: 0.000009\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Epoch 14/15: 100%|██████████| 469/469 [00:27<00:00, 17.18it/s, loss=0.0182]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 14/15, Loss: 0.0215, LR: 0.000002\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Epoch 15/15: 100%|██████████| 469/469 [00:27<00:00, 17.14it/s, loss=0.0252]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 15/15, Loss: 0.0216, LR: 0.000000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Training\n",
        "model = UNet().to(device)\n",
        "optimizer = torch.optim.AdamW(model.parameters(), lr=2e-4)\n",
        "scheduler = torch.optim.lr_scheduler.CosineAnnealingLR(optimizer, T_max=15)\n",
        "\n",
        "num_epochs = 15\n",
        "losses = []\n",
        "\n",
        "for epoch in range(num_epochs):\n",
        "    model.train()\n",
        "    epoch_losses = []\n",
        "\n",
        "    pbar = tqdm(train_loader, desc=f\"Epoch {epoch+1}/{num_epochs}\")\n",
        "    for x_0, _ in pbar:\n",
        "        x_0 = x_0.to(device)\n",
        "        loss = train_step(model, x_0, schedule, optimizer)\n",
        "        epoch_losses.append(loss)\n",
        "        pbar.set_postfix({'loss': f'{loss:.4f}'})\n",
        "\n",
        "    scheduler.step()\n",
        "    avg_loss = np.mean(epoch_losses)\n",
        "    losses.append(avg_loss)\n",
        "    print(f\"Epoch {epoch+1}/{num_epochs}, Loss: {avg_loss:.4f}, LR: {scheduler.get_last_lr()[0]:.6f}\")\n",
        "\n",
        "plt.plot(losses)\n",
        "plt.xlabel('Epoch'); plt.ylabel('Loss'); plt.title('Training Loss')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zY-8cE9aplrT"
      },
      "source": [
        "## 6. Sampling\n",
        "\n",
        "Sampling algorithm:\n",
        "1. $x_T \\sim N(0, I)$\n",
        "2. For $t = T, \\ldots, 1$:\n",
        "   - $z \\sim N(0, I)$ if $t > 1$, else $z = 0$\n",
        "   - $x_{t-1} = \\frac{1}{\\sqrt{\\alpha_t}} \\left( x_t - \\frac{1-\\alpha_t}{\\sqrt{1-\\bar{\\alpha}_t}} \\hat{\\varepsilon}_\\theta(x_t, t) \\right) + \\sigma_t z$\n",
        "3. Return $x_0$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "id": "_lUJaxCoplrT"
      },
      "outputs": [],
      "source": [
        "@torch.no_grad()\n",
        "def sample(model, schedule, n_samples=16, image_size=(1, 28, 28)):\n",
        "    model.eval()\n",
        "\n",
        "    x = torch.randn(n_samples, *image_size, device=schedule.device)\n",
        "\n",
        "    for t in tqdm(reversed(range(schedule.T)), total=schedule.T, desc=\"Sampling\"):\n",
        "        t_batch = torch.full((n_samples,), t, device=schedule.device, dtype=torch.float)\n",
        "\n",
        "        epsilon_pred = model(x, t_batch)\n",
        "\n",
        "        alpha_t = schedule.alpha[t]\n",
        "        alpha_bar_t = schedule.alpha_bar[t]\n",
        "        sigma_t = schedule.sigma[t]\n",
        "\n",
        "        if t > 0:\n",
        "            z = torch.randn_like(x)\n",
        "        else:\n",
        "            z = 0\n",
        "\n",
        "        x = (1 / torch.sqrt(alpha_t)) * (x - (1 - alpha_t) / torch.sqrt(1 - alpha_bar_t) * epsilon_pred) + sigma_t * z\n",
        "\n",
        "    x = torch.clamp(x, -1, 1)\n",
        "    x = (x + 1) / 2\n",
        "    return x"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "id": "kXM6xCJ1plrT",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 586
        },
        "outputId": "93008dc6-ca65-44b8-edb6-7e3ef00f90c9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Sampling: 100%|██████████| 1000/1000 [00:10<00:00, 95.04it/s]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x1000 with 64 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Generate samples\n",
        "samples = sample(model, schedule, n_samples=64)\n",
        "\n",
        "fig, axes = plt.subplots(8, 8, figsize=(10, 10))\n",
        "for i, ax in enumerate(axes.flat):\n",
        "    ax.imshow(samples[i, 0].cpu().numpy(), cmap='gray')\n",
        "    ax.axis('off')\n",
        "plt.suptitle('Generated Samples', fontsize=16)\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rBOHto4OplrT"
      },
      "source": [
        "## 7. Visualize the Denoising Process"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "id": "ZuuTATjzplrT",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 293
        },
        "outputId": "2e7e2940-0690-410a-83b8-285d3349c381"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1600x800 with 32 Axes>"
            ],
            "image/png": 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N0qdPLwsWLHhnGR8fH/n888/lzp070rBhQ/ib/q9evZIff/xRHj58+Le3qVOnTuLi4iKnTp2SMWPGiGEYcV87ffq0jBo1SkRE+vTp85frev36tUyePBl+FsaBAwckLCxMkiZNKpkyZfrb2635+uuvJUmSJLJq1SrZtGnTO19bv369/Pzzzwn22GZ98803YmtrKxs3bpQVK1a887Vdu3bJvHnzRESkd+/ecd3W1lYGDhwoIiKdO3eW33777b31Hj9+PO6zN0REhg4dKnZ2dtKnTx9ZunQp/JDy8+fPy/r16+P+/4YNG+S33357b9moqCjZsWOHiIhkzZo1rk+cOFFu37793novX74s165de295IiIiIqJPGf9ZJyIiIiL6x1q4cKHs379fRP7zIdRPnjyRU6dOxf0TSb6+vrJ48WL4hq2/v7+EhYXJ9u3bJU+ePFK4cGHJli2bGIYhwcHBcubMGXn79q1cunRJ0qZN+7e2M23atPLjjz9K48aNZeDAgbJ8+XLx8fGRR48eSUBAgERHR0v79u2lU6dOf7mut2/fynfffSd9+vSRggULSq5cuSRZsmQSHBwsR44cERGRgQMHioeHx9/a5g8pWrSojBo1Sr7//nupX7++lCpVSrJnzy7Xr1+XY8eOyXfffSeTJk0SOzu7BNuG+CpYsKDMmjVLunXrJq1bt5YpU6aIl5eX3Lp1Sw4fPiyGYciwYcPe+We/RP5zU+PKlSsyd+5cqVixovj4+EiePHnk+fPncf9E1759++JuAhUpUkRWrFgh7dq1k3bt2smgQYMkX7584uHhIaGhoXLu3DkJCQmRpk2bSsOGDUVEJCAgQKZNmybu7u7i4+MjadKkkRcvXsiRI0fk0aNHkjFjRunbt2/cNo0aNUr69OkjXl5ekjdvXnF0dJR79+7JwYMHJTo6Wtq0aSNFihSx3pNLRERERPQ38OYEEREREf1jHTp0SA4dOiQiIk5OTuLq6ioFCxaUYsWKSdOmTaV48eLq9zo7O8uuXbtk9erVsmLFCjl58qQEBgaKi4uLpE+fXlq2bCl169a12L/fX6dOHTl16pT88MMPsmfPHlm3bp04OTlJ+fLlpUuXLtK0adN4rSdFihQyd+5cCQgIkNOnT8vu3bvl7du3kiFDBmnYsKF8+eWXUrlyZYts84cMGDBAvLy8ZNKkSRIYGCgXLlyQwoULy8aNGyVVqlQyadIk05+9kFA6d+4shQsXlokTJ8rBgwfl7Nmz4urqKrVq1ZJvvvkm7p9k+jMbGxuZM2eO1KtXT+bOnStHjhyR8+fPi5ubm2TLlk3atm0rhQoVeud7GjduLMWLF5fp06fL7t275dChQxITEyNp06aVnDlzytdffy2NGjWKW75du3bi6OgoBw8elIsXL0pAQIC4urpKlixZ5Ntvv5XOnTtL6tSp45afNWuW7NmzR44fPy4BAQHy6tUrSZcunVStWlU6d+4s9erVS7gnkYiIiIjIwmyMP/9NORERERER0d80YsQIGTp0qHTv3l2mT5+e2JtDRERERESfIH7mBBERERERmXbt2jV59uzZe/2XX36RsWPHio2NjbRt2zYRtoyIiIiIiP4J+M86ERERERGRaT/++KOMGTNGfHx8JHPmzBIVFSVXrlyRK1euiIjIsGHDpGjRoom8lURERERE9KnizQkiIiIiIjKtRo0acu3aNTly5IhcunRJIiIiJHXq1OLn5ydffvml1KhRI7E3kYiIiIiIPmH8zAkiIiIiIiIiIiIiIrIqfuYEERERERERERERERFZFW9OEBERERERERERERGRVfHmBBERERERERERERERWRVvThARERERERERERERkVXx5gQREREREREREREREVkVb04QEREREREREREREZFV8eYEERERERERERERERFZFW9OEBERERERERERERGRVfHmBBERERERERERERERWRVvThARERERERERERERkVXx5gQREREREREREREREVkVb04QEREREREREREREZFV8eYEERERERERERERERFZFW9OiMjhw4dl2LBhEhYWZpH1rV69Wlq1aiW5cuUSGxsb8fX1VZeNjIyUfv36SYYMGcTR0VFKliwpu3fvVrezXLlykjx5ckmXLp306NFDXr58+bfWSWSGpcdKRESEjB07VvLlyyfJkyeXjBkzSuPGjeXChQvvLRsWFiadO3cWDw8PcXJykkqVKsmpU6fgen/55RcpUqSIODg4SJYsWWTo0KESHR1tkW0m+m+WHhciIi9evJC+fftKtmzZxN7eXjJmzCiNGjWS169fv7McxwV9qhJiXPzhxo0b4uDgIDY2NnLixIn3vs5xQZ8qS46Lp0+fyoQJE6RChQri4eEhbm5uUqpUKVm9ejVcPiGuOYgs4d92LU6UkCw9Xjw9PcXGxua9/7p27fresmbmV0SJLSGuRXjdkIAMMiZMmGCIiHHz5k2LrK9ixYpGihQpjEqVKhkpU6Y0KlasqC7brFkzw9bW1ujdu7cxb948o3Tp0oatra1x4MCBd5Y7ffq04eDgYPj4+Bhz5swxBg4caNjb2xs1atT46HUSmWXpsdKwYUPD1tbW6Natm7FgwQJj+PDhRpo0aQxnZ2cjODg4brmYmBijTJkyhpOTkzFs2DBj5syZRr58+QxnZ2fj6tWr76xz27Ztho2NjVGpUiVj/vz5Rvfu3Y0kSZIYXbt2tcg2E/03S4+LsLAwo3Dhwkbq1KmNAQMGGIsWLTLGjRtn1K5d2wgNDY1bjuOCPmWWHhd/5ufnZzg5ORkiYhw/fvydr3Fc0KfMkuNi8+bNRrJkyYx69eoZU6dONWbOnGlUqlTJEBFjyJAh7y2fENccRJbwb7sWJ0pIlh4vWbNmNby9vY3ly5e/89/Ro0ffWc7M/IroU2DpscLrhoTFmxOG5Xfa27dvGzExMYZhGEb+/PnVCdHRo0cNETEmTJgQ1968eWPkyJHDKF269DvL1qxZ00ifPr0RHh4e1xYsWGCIiLFz586PWieRWZYcKyEhIYaIGL17936n79271xARY/LkyXFt9erVhogYa9eujWuPHj0y3NzcjObNm7/z/fny5TMKFy5sREVFxbWBAwcaNjY2xqVLl/72dhP9N0ufQ7p162a4ubkZQUFBH1yO44I+ZQl1c2LHjh2GnZ2dMWjQIHhzguOCPmWWHBdBQUHv/CKHYRhGbGysUblyZcPe3t54+fJlXE+Iaw4iS/k3XYsTJbSEuDlRu3btv1zOzPyK6FNg6bHC64aE9T9/c2Lo0KGGiLz3n6V24A9NiPr06WMkTZr0nUmOYRjGmDFjDBExbt++bRiGYYSHhxu2trZGnz593lkuMjLSSJEihdGhQwfT6yQyy9Jj5dKlS+9dEPy5z5kzJ641btzYSJs2bdyFxh86d+5sJE+e3IiIiDAMwzAuXLhgiIgxa9asd5a7e/euISLGyJEjP2pbiTSWHhfPnj0zHBwcjL59+xqG8Z/j/B/793/juKBPVULNrd6+fWvkyZPH6NOnj+Hv7w9vTnBc0Kcqoa85/jB9+nRDRIyzZ8/GtYS45iCyhH/btThRQkqI8fLHzYnIyMh3bmr/t/jOr4g+BZYeK7xuSHi28f8HoP6dGjZsKFevXpWVK1fKlClTxN3dXUREPDw8JDw8XKKiov5yHQ4ODpIiRQrTj3369GnJnTu3uLi4vNNLlCghIiKBgYGSOXNmOXfunERHR0uxYsXeWc7Ozk68vb3l9OnTptdJZJalx0qOHDkkU6ZMMmnSJMmTJ4/4+PjIvXv34v6d/WbNmsV93+nTp6VIkSKSJMm7H5NTokQJmT9/vly9elUKFiwYNxb+e6xkyJBBMmXK9M5YIbIES4+LgwcPSkREhOTMmVMaNWokGzdulNjYWCldurTMmjVLvL29476P44I+VQk1t5o6dao8e/ZMBg0aJOvXr4ffx3FBnyprXXM8ePBARCRu/SIJc81BZAn/tmtxooSUUONl7969kjx5comJiZGsWbNKz5495ZtvvnlnmfjOr4g+BZYeK7xuSHj/8zcnChUqJEWKFJGVK1dK/fr1xdPTM+5rvr6+EhAQ8JfraNu2rSxZssT0Y9+/f1/Sp0//Xv+j3bt3L265P/f/XvbAgQOm10lklqXHSrJkyeTnn3+WFi1aSN26deOWKVq0qBw+fFjc3Nzi2v3796VChQrvre/P+3XBggX/cqxw/ydLs/S4uHbtmoiIDBgwQHLkyCHLli2T8PBwGT58uFSuXFkuXLgQt39zXNCnKiHmVg8ePJCRI0fKxIkT33sj6c84LuhTZY1rjtDQUFm4cKGUL1/+nX07Ia45iCzh33YtTpSQEmK8FCpUSMqVKyd58uSRp0+fypIlS+Tbb7+Ve/fuyQ8//BC3XHznV0SfAkuPFV43JLz/+ZsTHzJp0iR59uzZXy6XIUOGj1r/mzdvxN7e/r3u4OAQ9/U//6+27B9fN7NOIkv62LGSMmVK8fb2lsaNG0upUqXk+vXrMnbsWGncuLHs3r37nf3WEmPl+fPn5n4wor/hY8bFy5cvRUTExsZG9uzZE/fbGj4+PnF/PTFq1CgR4bigf6aPPV/069dPsmfPLh07dvzg93Fc0D+RJa45YmNjpWXLlhIWFiYzZsx452sJcc1BlND+idfiRInlY8fLL7/88s7/b9++vdSsWVMmT54s3bt3l0yZMokI32eif4+PGSu8bkh4vDnxAUWLFk3Q9Ts6OkpkZOR7PSIiIu7rf/5fbdk/vm5mnUSW9DFjJTw8XMqXLy99+vSR7777Lq4XK1ZMfH19xd/fX7p16yYiCTNWiBLax4yLP/ZRPz+/d/7kulSpUpItWzY5fPjwO8tyXNA/zceMiyNHjsjy5ctlz5497/1zAv+N44L+iSxxzdG9e3fZsWOHLFu2TAoXLvzO1zgu6J/on3gtTpRYLDVebGxspGfPnrJz507Zv3+/tGrVSkT4PhP9e/yda3SeBxIOb058QGhoqLx9+/Yvl3N0dBRXV1fT60+fPr3cvXv3vf7Hnwz9cafuz/+EB1r2z3f04rtOIkv6mLHy888/y8OHD9/5J51ERCpWrCguLi5y6NChuJsT6dOnV/d/ETxW/vuzVe7fvx/3b8gSWcPHjIs/9uW0adO+t1yaNGne+S0Pjgv6J/qYcdG3b18pX768ZMuWTYKDg0VE5MmTJyLyn3349u3bkiVLFhHhuKB/pr97zTF8+HCZPXu2jBs3Tlq3bv3e1xPimoMoof0Tr8WJEoslx8sf86LQ0NC4Ft/5FdGn7mPGCq8bEt6Hf/3sf4SNjQ3sDRs2lPTp0//lf//9YUHx5e3tLVevXn3vT4COHj0a93URkQIFCoitra2cOHHineXevn0rgYGB73xAanzXSfQxLDlWHj58KCIiMTEx76zLMAyJiYmR6OjouObt7S2nTp2S2NjYd5Y9evSoJE+eXHLnzh23nIi8N1bu3bsnISEh3P8pQVhyXPzxmxzoYvnevXvi4eER9/85LuhTZslxcfv2bfntt98kW7Zscf/16dNHRETq1q0rhQoViluW44I+ZQlxzTFr1iwZNmyYfPvtt9KvXz+4/oS45iCylH/TtThRQrPGeAkKChIR+ajrDqJPhSXHCq8bEh7/ckJEnJycREQkLCzsnZ7Q/85lo0aNZOLEiTJ//nzp3bu3iPznz4T8/f2lZMmScXfkXF1dpUqVKrJixQoZPHiwODs7i4jI8uXL5eXLl9K4cWPT6yT6GJYcK39MYFatWiXDhg2L67/88ou8evVKfHx84lqjRo1k3bp1sn79emnUqJGI/Oe3ZteuXSt+fn5x//Zf/vz5xcvLS+bPny9dunSRpEmTiojInDlzxMbGJu57iSzJkuMiT548UrhwYdm0aZM8efJE3N3dRURk165dcufOHenevXvcshwX9Cmz5LiYP3++vH79+p2v7927V2bMmCETJ04ULy+vuM5xQZ8yS19zrF69Wnr06CEtW7aUyZMnq9+XENccRJbyb7oWJ0polhwvoaGh4urqGjcHEhGJioqScePGiZ2dnVSqVCmux3d+RfSpsORY4XWDFRhkHDt2zBARo1atWsayZcuMlStXGi9fvvzo9QUEBBgjR440Ro4caaRJk8bw9PSM+/8BAQHvLNu4cWPD1tbW6NOnjzFv3jyjTJkyhq2t7XvLnTx50rC3tzd8fHyMOXPmGAMHDjQcHByMatWqvff48V0nkVmWHCuRkZFG/vz5DRsbG6Ndu3bG3Llzjd69exsODg5G+vTpjcePH8ctGx0dbZQqVcpIkSKFMXz4cGPWrFlG/vz5DWdnZ+Py5cvvrHfz5s2GjY2NUblyZWP+/PlGjx49jCRJkhidOnX6Wz87kcbS55C9e/caSZMmNfLkyWNMnjzZGDp0qOHs7Gzkzp3bePHiRdxyHBf0KbP0uPhv/v7+hogYx48ff6dzXNCnzJLj4ujRo4adnZ3h4eFhLF682Fi+fPk7/924ceOd5RPimoPIEv5t1+JECcmS48Xf39/IkSOH0a9fP2Pu3LnGmDFjjAIFChgiYowZM+adZc3Mr4g+BZY+t/C6IWHx5sT/N3LkSCNjxoxGkiRJDBExbt68+dHrGjp0qCEi8L+hQ4e+s+ybN2+M3r17G+nSpTPs7e2N4sWLGzt27IDrPXDggFGmTBnDwcHB8PDwML766ivj+fPn7y1nZp1EZllyrISGhho9e/Y0cufObdjb2xvu7u5Gs2bNjKCgILhshw4djNSpUxvJkyc3Klas+N6bUn/YsGGD4e3tbdjb2xuZMmUyBg0aZLx9+/ajt5Por1hyXBiGYezevdsoVaqU4eDgYKRKlcpo3bq1cf/+/feW47igT5mlx8WfaTcnDIPjgj5tlhoXf4wB7T9/f/93lk+Iaw4iS/k3XYsTJTRLjZcTJ04Yfn5+RsaMGQ07OzsjRYoURrly5Yw1a9bA5c3Mr4g+BZa+FuF1Q8KxMQzDSMi/zCAiIiIiIiIiIiIiIvozfiA2ERERERERERERERFZFW9OEBERERERERERERGRVfHmBBERERERERERERERWRVvThARERERERERERERkVXx5gQREREREREREREREVkVb04QEREREREREREREZFV8eYEERERERERERERERFZle3fXYGNjQ3shmHAvmXLFtj9/PxMrcfFxQX2X375BfbDhw/DHhkZCfv48eNhDw0Nhb19+/awJ0+eHPbVq1fDLiKyadMm2NevXw/7nDlzYN+1axfs1apVg33t2rWwN2jQAPb79+/D3qlTJ9i3b98O+4EDB2APCAiAfdCgQbAnhi5dusAeExMD+8KFC2HXxlGqVKlg7927N+zafn758mXYDx06BHvatGlh79u3L+zafv7DDz/Afv78edhz5MgBu4hIuXLlYNee0wEDBsA+cOBA2IsVKwZ79+7dYZ8+fTrsDRs2hH3Dhg2wa6pUqQL78+fPYQ8MDIRdO8YlJE9PT9hTpkwJ++nTp2HXxkWzZs1g1/bbEiVKwN6yZUvYtWNeUFAQ7GfOnIFdO39px9qmTZvCvm3bNthFRH7++WfY3759C/uyZctg157T48ePw37jxg3YS5UqBfv169dhf/LkCezaOV47j3zzzTewDxkyBHZtzpGQhg0bBvvt27dhX7x4Mey1atWCXdtPfH19YdfmDi1atIA9Z86csK9btw52Ozs72LVjkjbeP0bJkiVhP3r0KOxVq1aFXZtH1alTB/atW7fGY+v+z6pVq2D/6quvYNfOgzt27IC9T58+sI8cOTIeW2c9adKkgf3x48ewa+fx0aNHm3rcpEmTwq7N4bQxoM3VLl68CHvFihVh79+/P+zavFqb232Idow+cuQI7Pny5YM9SRL8+20RERGwa+eAMmXKwK7NdbT5oyZTpkywh4SEwF6kSBHYT548aepxLSFLliyw37lzB3YvLy/Y37x5A/utW7dgT506NexPnz6F3d3dHXbt/G5ri99+SJcuHezaPnLq1CnYtX3tQ5ydnWHX5q3JkiWDXZsbadc32vLa+IqNjYXdrPTp08OuXdtrx43ff//dIttjhqXmCgUKFIBdO8Zox3/tWOLo6Ai7Nj9/9eoV7GYl9L4jYv79P43Z18BS3NzcYA8LC7PI+s0+D5ZgyTk0UUKIz7jgX04QEREREREREREREZFV8eYEERERERERERERERFZFW9OEBERERERERERERGRVfHmBBERERERERERERERWRVvThARERERERERERERkVXZxnfBmTNnmlqx9onxDRo0gL1s2bKw9+jRA3YHBwfY79+/D3u6dOlg79ChA+w//fQT7MmTJ4e9atWqsG/fvh326dOnwy6iPxfaYxQoUAD2sWPHqo+BfPXVV7A3btwY9ubNm8Pu6OgI+6pVq0ytR7Nx40bYT5w4YWo9llC9enXY582bB7s2LgoVKgT71q1bYR82bBjsu3btgv3t27ewP3nyBHbN5cuXYd+9e7ep7dHG9aZNm9THrlevHuxeXl6wG4ahrsuMe/fuwZ4tWzbY165dC/v69eth117LGzduwG5riw/bYWFhsCeGSZMmwX7gwAHY9+7dC3vHjh1h147bpUuXjsfW/Z8BAwbAni9fPthbtWoFe8mSJWEfP3487P369YP96NGjsH/otZ01axbsXbt2hX3z5s2w+/n5qY9hRpIk+HceChYsCLt2/O/UqRPs2jFUG+/u7u6wmz32WULOnDlhDw8Ph71cuXKwHzp0CHbtOT5//jzs8+fPhz1NmjSwr1u3DnYPDw/YtfFldm6i7f9ubm7q9xQpUgR2bYxp5yptf9MsXLjQ1PLNmjWDfdCgQbCPHDkSdm07Hz16BPvQoUNhHz58OOwJrV27drBr88ZTp07B3rdvX9iXLFkCu/b8aK5fv25q+TJlysB+6dIl2MuXL29q/RUrVoRdu1YR0eeb2ji7ePEi7MmSJYNdOx44OTnBrh0Xly1bBru2/fnz54d95cqVsGvnmHPnzsGeGHx9fWF/8eIF7AEBAbBr15W3bt2C/enTp7CnSpUKdrPn0+joaNhDQkJgf/bsGezaeNTeI4iIiFC3KW/evLDfvXsXdu1ndnZ2hl2b03t6esIeHBwMu1naNZJ2PaddY1y9etUi22MJKVOmhP3Vq1ew29vbwx4aGmpq/c+fP4dd26+0rs2TzdL2czs7O9i17f/Q+SJp0qSwa/NEbT/XBAUFwZ45c2bY79y5Y2r9GrPXzHny5IFdO4YS0cfhX04QEREREREREREREZFV8eYEERERERERERERERFZFW9OEBERERERERERERGRVfHmBBERERERERERERERWRVvThARERERERERERERkVXZxnfByMhI2A3DgD1//vywp0qVCvbChQvDPmTIENiLFy8Oe4sWLWDXtrNDhw6m1nPx4kXY8+XLB3upUqVgX7ZsGewiIo8ePVK/hlSpUgX23Llzw96zZ0/YZ86cCfvYsWNhDwwMhP2LL76AXdOsWTPYbWxsYD958qSp9SekEiVKwL5p0ybYtf1QM2fOHNhr1qwJe1BQEOx79+6FvVOnTqa2Z/Xq1bD/8MMPsJcvX97U+rdu3ap+bfLkybCfO3cO9kmTJsF++vRp2KtXrw77zz//rG4TUqxYMVPLDx8+HPb9+/fD7uvrC3uWLFlgf/z4santsYTly5fDvmbNGtjt7OxgP3PmDOxly5aFvUGDBrB7eHjAXr9+fdi3b98Ou4+PD+xv376FvW/fvqa259dff4V93759sIvo++3SpUthv3HjBuzacbhgwYKwDxw4EPbXr1/D3qdPH9htbfE0RDv+a9s5bNgw2I8fPw57YmjdujXs7du3h/3gwYOwJ0+eHHZtXzh//jzs2n6YMmVK2B0cHGAvWbIk7Nqcws3NDfbRo0ebWv5DtHPngAEDYL969Srs2jlbm4NOnz4ddm1caEaNGgX7rFmzYNfm1to4un//vqntSWjaXGHChAmwN2zYEHZ/f3/YixYtCvu9e/dgP3v2LOwLFiyAXZtLHT58GPYePXrAvn79etjr1asHu7Y/fPbZZ7CL6PM1TUBAAOxPnz6FXTvO+fn5wf6h6yFEe20yZ85saj0hISGwp0iRwtR6ElLSpElh/+2332B/9uwZ7Nqxu0CBArBHRETAfv36ddi9vLxgf/DgAexhYWGwa7TjVZ48eWC/cuUK7Pb29upjHDt2zNQ2aXP9EydOwJ42bVrYtes57RyWLl062LXn+tWrV7BrcubMCbs23hNDVFQU7Np88sWLF7BrY/3NmzewJ0limd/pjY2Ntch6tHGqrV87npidn4iIxMTEwK4da7RtzZAhA+za8Vm71r19+zbs2jxXOxZoj6sds7TrPyL6OPzLCSIiIiIiIiIiIiIisirenCAiIiIiIiIiIiIiIqvizQkiIiIiIiIiIiIiIrIq3pwgIiIiIiIiIiIiIiKr4s0JIiIiIiIiIiIiIiKyKhvDMIz4LHjx4kXYnz9/Dvvhw4dhb9y4Mey3bt2CvVy5crBfv34d9ho1asB+48YN2AsUKAC7vb097Nu2bYM9bdq0sP/444+w+/v7wy4iMn36dNjz5cunfg8Sz5c2TkREBOyOjo6w3717F/YVK1bA3q9fP1PbozH7cyWGvn37wp48eXLYhw0bBnvevHlhd3d3h/3gwYOwHzhwAHZtfAUFBcEeFhYGe4sWLWBv1qwZ7Nq+ZmNjA7uISNmyZWE/evQo7MeOHYN9586dph5bG/OLFi2Cfd26dbAPHToU9mTJksFeuXJl2KdNmwb7mjVrYE+M8XL8+HHYteOktnx4eDjsHTp0gF17TS5fvgx73bp1Ye/Zsyfs2vhycHCAvVKlSrBr427EiBGwZ82aFXYRka5du8L+9ddfw54rVy7YW7VqBfuTJ09g9/b2hn3AgAGwv3nzBnbtfKftK9r4unnzJuznzp2DPTIyEvaEpB1jtOPhuHHjYNdew5YtW5ranqRJk8J++vRp2LXX1snJCfaNGzfC3qZNG9i1eV1oaCjsfn5+sIuIeHl5wa7t54ULF4ZdO64uWbIE9levXsGuzZW1uamzs7Op9WvL9+nTB3ZfX1/YE2t+1bx5c9grVKgAu3aMbtiwIezavqgdlzJlygR70aJFYdfmw9q85eTJk7Br55hq1arBvmvXLtg/++wz2EVE5s2bB3vOnDnV70G0816SJPj33rQ5jbYvzpkzB3ZtzGjXbdqxfsiQIbBr5+HEGBvaOaN169awb9iwAXbtHJM9e3ZTy9++fRt2s7R9TTu+aeeYkJAQ2KOjo2F3c3NTt0mb66ROnRr2YsWKwX7nzh3YX79+DXu2bNlgP3HiBOwvXryAXZMhQwbY7927B3vt2rVhP3XqlKn1JCRtrKdMmRL2hw8fJuTmJDhXV1fYtWsk7bihHcO069APrStz5sywa2NYOw7HxMTArr3Gjx8/ht2sVKlSwa7NN7X34LT3Rz+l8wXRpyI+44J/OUFERERERERERERERFbFmxNERERERERERERERGRVvDlBRERERERERERERERWxZsTRERERERERERERERkVbw5QUREREREREREREREVmUb3wXbtm0L+/Hjx2EfPHgw7L169YK9fPnysOfLlw/2GjVqwF6zZk3YZ86cCfv58+dh1/z++++wBwYGwu7t7Q370qVL1cd49uwZ7La2+OWKjo6G3cbGBvb+/fubWo/2yeqTJ0+GvW/fvrBPmTIF9t27d8NevXp12MPDw2F3dXWFPSFpz7FGey537NgB+/fffw97jx49YO/Tpw/sXbt2hf3ChQuwd+zYEfYFCxbA3rJlS9iHDBkCu52dHezaPigi0qZNG9gjIyNhnzVrFuxbtmyB3dPTE/b58+fDvnHjRthTp04Ne6dOnWAvW7Ys7G/evIF93759sLu4uMCeGC5fvgz70aNHYW/YsCHs/fr1g10bR9p4HDFiBOxv376FXTuvbd68GXY/Pz/YkyZNCvvIkSNN9VKlSsEuoh8jKlWqBPvDhw9hz5MnD+wnTpyAXTuH5c6dG3bttdF+tiNHjsB+9uxZ2AsVKgT72LFjYU8MrVu3ht3BwQF2bT/XaMdhjTYvWr58OeyNGjWCXTsWauNr4cKFsNeuXRv2/fv3w649nx/6WtasWWF3c3OD3cvLC/bs2bPDHhQUZKpHRETAro2vrVu3wv7tt9/C7uvrC/unxsfHB/bSpUvDrp337927B7v2PDg5OcGuncM2bdoEe7du3WCfNm0a7J999hns2nZevXoVdo2zs7P6tZw5c8KujY1bt27Bru272vq1uVeGDBlg166rtHNSz549YQ8ODoZdmxd8SmNGe0208/jLly9hL1KkCOynTp36uA2LJ20+oG2nvb097C9evIBdO0dq1xLa8yAismvXLti1Y83OnTth18ae9jM0bdoUdm3+qF0za3OdefPmwa45ffo07I6OjqbWk5C0633tOfvUaOPi0aNHsD9//hx2d3d32J88eWJqe6KiokwtLyISEhICuzZezNKujbXj85o1a2DXzs3a+UW79tB+3g+da4ksTbvW1cbLsGHDYJ8wYQLsEydO/KjtsiT+5QQREREREREREREREVkVb04QEREREREREREREZFV8eYEERERERERERERERFZFW9OEBERERERERERERGRVfHmBBERERERERERERERWZVtfBc8fvw47OfOnYP9/v37pjakRYsWsG/evBn2r7/+GvatW7fCPnPmTNgHDRoE++PHj2FPliwZ7A0bNoS9W7dusKdLlw52EZEbN27AvmnTJthr164Nu2EYsNvY2MDes2dPU8trevXqBbufnx/sXbt2hX3Hjh2wDxgwAPbZs2fHY+ssa+jQobCfPn0a9mnTpsHeuHFj2C9dugS79lwGBATAHh4eDvvOnTthf/ToEexffvkl7Npzf+3aNdhHjBgBe5o0aWAXEUmePDns27dvhz1Xrlywa+MiMDAQ9h9++AH2unXrwj5lyhTYs2fPDru/vz/s2muwZs0a2Fu1agV7YtCOGd27d4c9VapUsC9fvhz2lStXwl61alXYq1WrBrt27Bk5ciTs2nkkZcqUsM+aNQv28+fPw379+nXYf//9d9hF9OPhokWL1O9BtOdOO6cePXoU9ps3b8LetGlT2KOiomCvV68e7C9evIA9NDQUdm3f6t+/P+wJSTsOa3r06AH7+PHjYdeObYMHD4Z93rx5sJcqVQp2bfxq5zVtzqKN6969e8PepEkT2Ddu3Ai7iMiQIUNg18awdtzes2cP7NqY1M4X5cqVg10bX/v374ddmxN8/vnnsGvn5jdv3sCeWLRj4qRJk2AvUaIE7F999RXs2nn2t99+g33OnDmwb9myBfaFCxfCrp2XV6xYAbs2r8iWLRvswcHBsHt6esIuIlKnTh3YtZ9No53ntfOYdnxat24d7Lt374Zduz7T5nCpU6eGXTuOmj13JqTIyEjYd+3aBbutLb6sN3vucXNzgz0mJgb2YsWKwX7s2DHYtf1ZOw5o69e2J2vWrLBr72V8yMuXL00tr81RMmXKBPsXX3wBuzZONRcvXoQ9Ojra1Hq0n1eb5yYG7RjwqdHeM7p69Srs6dOnhz0sLAz2J0+efNR2/bcPvbbPnj2DXZu7m1WmTBnYtfeAtHO2Rntf4datW6bW4+joCHtsbKyp9RDFR/Xq1WHXrhnu3bsHu7u7O+z29vYft2FWwL+cICIiIiIiIiIiIiIiq+LNCSIiIiIiIiIiIiIisirenCAiIiIiIiIiIiIiIqvizQkiIiIiIiIiIiIiIrIq3pwgIiIiIiIiIiIiIiKrsv27KyhUqJCp5bVPB3/79i3s9+/fh/3XX3+F/ZdffoHdMAzYV61aBfumTZtgT5IE388JCgqCffbs2bBPnToVdhGRmjVrwl6lShXY7969C3ufPn1gv3LlCux58uSB/dmzZ7D7+fnBniJFCthfvXoF+86dO2Fv0KCBqfUnhtq1a8OuPcc7duyA/dtvv7XI9mj7uVk2Njawa/uCnZ0d7DVq1IB97dq1sDdp0kTdpg0bNsB+4cIF2OfNmwe7dowoUKAA7GPHjoVdG49bt26FvWjRorC3b98edu010KRJk8bU8gnp+fPnsB8+fBj2/v37w+7u7g57ixYtYO/WrRvsI0eOhL1w4cKw16lTB/Z27drBniNHDti17S9XrhzsXbt2hd3BwQF2EZEuXbrA/uDBA9irVq0K+7Fjx2DXzoW///477A8fPoRd259DQ0Nhnzx5MuytW7eG3cfHB3ZLHRMtoVWrVrBfv34d9i+++AL2/fv3w67NHUaPHg176dKlYdeOYS9fvoQ9WbJksAcGBsKujTvttdXOO4cOHYL9r76GXL58GfaFCxfCnjdvXtg7d+4M+7hx42DX5hAHDx6E/csvv4Rdmytrc+tevXrB/ql59OgR7No+rR2XtHlj/fr1Yf/8889hHz9+POzatdCaNWtgL1KkCOynT5+GXRtj2jnmQ9cYGu05atasGeza2KhXrx7sy5YtM7U927dvh107pmvzzePHj8Ouze20OWViMHu9o+2Hzs7OsN+4cQN2Nzc32F+/fg37zZs3Yc+aNSvs58+fhz1fvnywP3nyBPY3b97AHhkZCXvatGlhF9HPMyVKlID92rVrptYzadIk2MPDw2HXjt19+/Y1tT3aHCt16tSwa8cUbZ9IDI6OjrBr+0POnDlh144l2rjQnhvtvS3t/ZkMGTLAru3ntrb47Tpvb2/Y7927Z6pr+6yIfu7Rrvu193o02rlW2/+18ThmzBjYlyxZArs2Z9JER0fD/qHrM6K/or2vrL2foS2vneOnTJkCu3ZN8ingX04QEREREREREREREZFV8eYEERERERERERERERFZFW9OEBERERERERERERGRVfHmBBERERERERERERERWRVvThARERERERERERERkVXZGIZhxGfBGzduwJ4zZ07YW7VqBfuKFSviuWkf9tVXX8HesGFD2IOCgmDv2LEj7JUrV4Z93759sEdFRcFua2sLe4oUKWAXEXn16hXsjx8/NrV8oUKFYH/+/Dns2q4wYcIE2A8dOgT7xo0bYR82bBjsw4cPN7U9NjY2ppZPDEmS4Pt+sbGxsP/222+wa8+9s7Mz7D/99BPs06ZNg/2bb76BXdOtWzfYL1++DLs2Xo4ePQr7zp071cfW9tuJEyfC3rVrV9gfPHgA+6VLl2AfOnQo7NoxUXuOPDw8YNf222bNmsF+4sQJU9uTGONiz549sLdt2xb25cuXwz5v3jzYBw4cCLt2zEuXLh3s9+/fh107j4wYMQL277//HnZHR0fYV69eDXuTJk1g17ZTRKRWrVqwaz9DkSJFYN++fTvsqVKlgr1v376wFyxYEPby5cvD7ufnB3umTJlgL1q0KOza9mvPdf369WFPSNq5y6z+/fvDrv1MuXPnhl17bb28vGDXjvPaMcbT0xP2/fv3w/7o0SPYS5YsCXvVqlVhF9HniNp8adOmTbBr+8+yZctgX7RoEezdu3eHPSAgAPaZM2fCvm7dOtgzZMgAe5kyZWDXtr9169awJzTtOLBlyxZT6ylRogTsx44dg93V1RX28PBw2MeNGwe7NiazZMliqtvb28OunVM19erVU782fvx42LVzw+DBg2HXnqMvv/wS9smTJ8MeHBwMu3YOmDFjBuzlypWDvWbNmrBr8whvb2/YT58+DXtCstQ5w8nJCXZtXqq9JmZp5wAfHx/YteOwdu2kXUu/fPnyrzfuvxQoUAD28+fPw67N0bU5kDZP1Nbfp08f2LXzZ0REBOya/Pnzw37hwgXYkyZNCnt0dLSpx7UEs+NCey9G2/Y8efLAfuXKFVOPq829tPdzcuTIAbs299L2c+21Sp48Oewfej61r2nHf23+OGTIENgbNGgA++7du2HXxpH2XJg9lrm4uMCuvQehHVs/5hj0d1nqfEGWlzp1atj79esHe69evWDX3s+uVq0a7JY6l1tKfN6T4l9OEBERERERERERERGRVfHmBBERERERERERERERWRVvThARERERERERERERkVXx5gQREREREREREREREVkVb04QEREREREREREREZFV2cZ3wRw5csCufep2qlSpYP/6669hj4mJgX3OnDmwX7x4EfZZs2bBrunUqRPsw4cPh33EiBGwN2/eHPZ169bB3rVrV3Wb5s6dC3vr1q1h1z4Bfvfu3bCXLFkS9pw5c8L++vVr2O/fvw/7zp07Ydee0+rVq8Pu5uYGe3w+6d1abt68aWr5AQMGwJ4lSxbYN2/eDHt4eDjsTk5OprbHy8sL9ho1asCuPfe2tvhQ0qBBA9g3bNgAu7ZviohUrFgR9rx588K+aNEi2L/66ivYr169CvuRI0dgd3V1hd3DwwN2Tbdu3WCvU6cO7FmzZoX9hx9+MPW4CalKlSqmlu/Vqxfsp0+fhv3ly5ewa/unjY0N7Pb29rC/ffsW9oiICNg1ffv2NbV8pkyZYK9WrZr6Pdo5zM7ODvYnT57AnitXLtjXrFkD++PHj2EPDAyEffz48bBXqFAB9oCAANg1adOmhf3hw4em1pMYChQoALt2LKlUqRLsS5cuhb1z586wa8ftJk2awL53717YJ02aBHuLFi1g9/T0hP3p06ewa8fmD7225cuXh71s2bKwHzx4EHbttdHmptp+qx2DfH19Yddoc2vtfKHRXkttnpnQMmfODLv2erVq1Qp27XilzUU0Li4usGtzF83t27dh1+YzoaGhsGvzZG2+rZ1LRETy5Mmjfg3R5oPaeq5fvw67ts9FRUXBbva5njhxIuylSpWCXRt7+/fvN/W4CSllypSwP3v2DHZvb2/Yteu158+fw64do7Vr9Xv37sEeHBwMu5+fH+xFihQxtZ7cuXPDfvjwYdjTp08Pu4jI+fPnYdeO3aNGjYJde7/k0aNHsP/000+w79ixA/bs2bPDHhQUBPvAgQNhHz16NOwa7bVPDOnSpYM9LCwMdm2ur+3/2pxDo71/cu3aNdi184u2j2jLa/umg4MD7Np1q3bM/hjDhg2DvWnTprBr1yTauNDGaYoUKf564/5EO1Zq1zCaV69emVqe/jcNGjQIdu198SRJ8N8PrFy5EnbtHPlPxL+cICIiIiIiIiIiIiIiq+LNCSIiIiIiIiIiIiIisirenCAiIiIiIiIiIiIiIqvizQkiIiIiIiIiIiIiIrIq3pwgIiIiIiIiIiIiIiKrso3vglWqVIH922+/hd3Gxgb2kiVLwt66dWvYDcP4642Lx+Pu378fdjs7O9hr1qwJ+5AhQ2AvV64c7L169YL9Qz/XixcvYE+RIgXsDRs2hP327duwa5/03rx5c9i1bX3+/DnsixcvNrUe7TXTaMub3VcswcPDA/batWvDPnbsWFPr1/a3ESNGwN6qVSvY58+fD/vatWthN/tcRkdHw16gQAHYzY5TEZFOnTrBXq9ePdirVasGu7bfambMmAH75s2bYT969CjsJUqUgF17LubOnRuPrfs/2vNQpkwZU+uxBG3/SZ06NeyzZ8+G3eyxQXvNNW5ubrBPmTIF9hMnTsA+efJk2Pft2we7p6cn7M2aNYO9Y8eOsIuIPHjwAPYNGzbAXqRIEdhfvnwJe1RUFOwpU6aEffjw4bAHBATArp2nNGb3idWrV8PepUsXU+tJSOfPn4d9/PjxsFevXh12bX7l4+MD+8SJE2Hv3bs37Lt374Y9bdq0sH///fewazJkyGCq79y509T6RUTSp08Pu7at2mtz6tQp2LVzc7JkyWAvVKgQ7JkzZzb1uK9evYJdO8Zp535/f3/YE9qcOXNMLa89b87OzrBrx8NvvvkG9mnTppnanv79+8P++vVr2Pv06QP7qFGjYJ83b56p7QkJCVG/5uDgAHtERATsyZMnN7WegwcPwv7mzRvYtfO2NmayZ88Ou3adqvnQfPNT8ezZM9htbfHle5YsWWC/dOkS7JGRkbBr88arV6/CHhMTA7tG29e0xy1YsCDs2vFKmydox40PfU07z+TIkUNdF6L9zNr6ixUrBvuTJ09g9/Lygn306NHx2Lp/Fm3eq3FycoJdu4bXxoW2/PXr12HXzr/a+zza/EQ7RmrH1F27dsGubac2nxcRyZ07N+zaz9C0aVN1XYh2Xaidw9zd3WHXxoU2rgMDA/964+JBex+RLKdUqVKwf/7557CfPXsW9uXLl1tsmzTacVh7jzVJEvx3Atq1t/Ye7r8J/3KCiIiIiIiIiIiIiIisijcniIiIiIiIiIiIiIjIqnhzgoiIiIiIiIiIiIiIrIo3J4iIiIiIiIiIiIiIyKp4c4KIiIiIiIiIiIiIiKzK9u+uYODAgbDXqlUL9vXr18NuGAbsNjY2sB89ehT2mjVrwu7t7Q17uXLlYPf19YW9TZs2sB8/fhz2pUuXwl6iRAnYP0R7LrTnrlGjRrBXrFgR9k6dOsEeEhICe6ZMmWDv2bMn7LNmzYJ9+/btsE+ePBn2woULw54Ypk6dCvuWLVtg37lzJ+wxMTGwjxgxAvbx48fDPn/+fNinTJkCe/Xq1WE/d+4c7BkzZoT9+vXrsF+4cAH2Pn36wN6hQwfYRURu3LgBe6tWrWA/cuQI7HXq1IE9KCgI9saNG5taz7hx42Dv3r077GZ17twZ9jJlylhk/ZZw//592P39/WEvXbo07JMmTYJ9zpw5sGvjq2PHjrDv27cP9hYtWsCuPffa8X/jxo2wDx48GHZtO0eNGgW7iMigQYNg1/ZPHx8f2H/66SfYtfNF165dYdeOfdHR0bAHBwfDXq1aNdg1gYGBsGvn4MRw7do12Pfv3w/7ggULTK1fe821/Uo752u05/j777+HvXbt2rBr5/zMmTOb2p7Zs2erX9PmcGYfQ5vzafvn0KFDTS0/ffp02LU5a4oUKWCPjIyEXdv/nz59Cnti0c5fhw8fhl07drdv3x72U6dOwT5t2jTYe/fuDfvly5dh79atG+xZsmSBXTtHzp07F/Zbt27BvmPHDti1c5iIyKZNm2DXrqu+/PJL2H/88UfYb9++DfvVq1dhf/bsGeyPHz+GPXv27LC/fPkSdu21Wb16Nez29vawf0q08+nu3bthb926NezaPFk7j2vXfRptDqdtj/aa58uXD3ZtH0yWLBnsERERsIuIBAQEwK7N6TXa9dyZM2dg145Nnp6esNva4rdutHGk+eabb2DXjg/aXO1Tor1Poj03Hh4esIeHh5vqTk5OppbXxoX2/smLFy9g1+YDSZLg3z3Wlv/QvqOdF7SfQZtbpE6dGnbtuH3w4EHYtWNQ2rRpYT979izsjo6OsJcvXx52bc7x9u1b2Mk8bd41evRo2O3s7GDXzo/aewSPHj2Kx9bFT7t27WDX9k/tPVztOK9dR/6b8C8niIiIiIiIiIiIiIjIqnhzgoiIiIiIiIiIiIiIrIo3J4iIiIiIiIiIiIiIyKp4c4KIiIiIiIiIiIiIiKyKNyeIiIiIiIiIiIiIiMiq8EeBAw0bNoT9q6++gv2zzz6Dffny5bDb2NjArn2KeZUqVWDfs2cP7Llz54bd3t4e9k2bNsHep08f2C9dugS7Rvt5P8TPzw/29evXwx4WFgZ7jx49YNee6wkTJsDet29f2LXnQnvcmjVrwq7ZtWuXqeUTUps2bWCfN28e7DVq1IC9f//+sI8dOxb227dvw/7o0SPYkyZNCvvq1athnz17Nuznz5+HvVKlSrA3btwYdm3f/Prrr2EX0bd1xYoVsGvHmtatW8PevXt3U4+bIUMG2F++fAl78+bNYf/2229h14412nOt7YvLli2DPSG1b98e9s8//xx27Xjo5eUFu7ZfabTz18KFC2HX9nM3NzfYp0yZAvvKlSthP3r0qKn1Fy5cGHYRkc2bN8Pu4+MD+4EDB2BfsmQJ7GnSpIG9dOnSsI8aNQr2hw8fwq5t57Bhw2DXBAYGwt6pUydT60lI2v7g7e0N+6BBg2DXxtepU6dgf/HiBey+vr6wP3/+HPaQkBDYtdc2VapUsC9evBh2bV/WFCtWTP2ak5MT7L169YJdm/+UL18edhcXl7/Yundp54ty5crBfvDgQdifPHkCe5cuXWDfuXMn7NoxMbGkTJkS9lWrVsF+4sQJ2FOnTg37tGnTYO/cuTPsEydOhD1r1qywa8fPIUOGwP7gwQPYnZ2dYdf22x07dsCuzX9ERIoUKQL74MGDYddeg7t378Lu6empPjby+PFj2LX58oYNG2Dv1q0b7HPmzIG9QYMGsLu7u8P+KdGOb69evYL9+PHjsEdERJh6XO0ckClTJti1uZSHh4epro0vbT6sHfe0c9WH3Llzx9Ty2s+cLl06U+sJDg6G3c7ODva3b9/Crr022jGxaNGiprYnMWj7iTZ30c7vtrbxfhtMRESSJMG/06uNuxQpUsD+7Nkz2LXzvjbX0d6fyZ49O+y3bt2CXXs+RfTjszaWtP3z9OnTsOfMmVN9bOT+/fuwa+/naSIjI2HX3mPSzs0xMTGmHpd0rq6usJsdp/7+/rBr+7IlaXN07Rik0Y4R/wv7G/9ygoiIiIiIiIiIiIiIrIo3J4iIiIiIiIiIiIiIyKp4c4KIiIiIiIiIiIiIiKyKNyeIiIiIiIiIiIiIiMiqeHOCiIiIiIiIiIiIiIisKt4ff75mzRpTK162bBnsU6ZMgf2bb76B3cbGBvbevXvD/vPPP8MeEBAA+8uXL2FfuHAh7IcPH4b9+PHjsJcuXRr2ihUrwi4iUqNGDVPrOnfuHOy//vor7NpzqvXLly/DnjdvXthPnDgB+65du2Bv164d7D4+PrC/ffsWdjs7O9gTUuvWrWHPkCED7LNnz4bdz8/P1ONu2bIF9k2bNsGeNGlS2FOnTm1qPdmzZ4f9iy++gH3cuHGwjx07FvYlS5bALiISGhoK+9mzZ2GvW7cu7NOmTYO9adOmsM+YMQN2wzBg12jja/78+bBr+5Y2rrVxkRh27NgBu/YcaM/liBEjYE+VKpWp7dGO/ylSpID98ePHsJcvXx727777DvZRo0bBvmjRItjDwsJgz507N+wiIhMnToS9b9++sJcrVw527ViQL18+9bERf39/U8ubpb023bt3h33nzp2w//TTTxbbpvgaMmQI7JMmTYK9WbNmsGvn3vXr15vaHm08pkmTBvapU6fCvmfPHtgbNGgA+8CBA2EPDg6G/dKlS7Brz4OISM+ePWHXjjXanPXAgQOwa8/dnDlzYO/WrRvsmqJFi8J+8uRJ2OfNm2dq/a6urrDXqVPH1HosZevWrbBXqlQJ9uLFi8N+4cIF2G/dugV7+vTpYX/69Cnsvr6+sHft2hV2jTa/dXBwgD1z5sywN2/eHPaVK1ea2h4R/XyrnRsOHToE+9q1a2HXfgZvb2/Yd+/eDbt2fHJxcYFds2HDBth//PFHU+tJDK9evYLd7HVcZGQk7B4eHrBr8wHtWlqbh2i0a4C9e/fCHhgYCHvOnDlh156HD9HGvPYza6ZPn276sRGzc31tfIWEhMCuvaeQJMmn8/us2jxQ4+npCfuDBw9MrSc2NhZ2Jycn2KOiomCvWbMm7Nr7PG/evIFdu9bS9pGYmBjYzT6fIvq5ytYWv7WonfPMzjm0n+H169ewZ8yYEfa7d++aelzt2KrtE6TT3pOqXbu2qfVo56+ZM2fCbvZ9m4+h7W8abb/q2LGjJTbnH+nTOdMQEREREREREREREdH/BN6cICIiIiIiIiIiIiIiq+LNCSIiIiIiIiIiIiIisirenCAiIiIiIiIiIiIiIqvizQkiIiIiIiIiIiIiIrIq2/guGBAQAHuqVKlgf/LkiakN0T6t/PPPP4f9s88+g71Hjx6wZ8+eHfZhw4aZWj4qKgr2EiVKwN6mTRvY+/XrB7uISL58+WDXPpX+8uXLsGvPab169WDfuHEj7KNGjYJ90KBBsI8cORL2OnXqwD5w4EDYz5w5A7u9vT3shmHAnpDKli0Le6dOnWDPmTMn7OHh4bA7Ozub2h5tPJ46dQr2bdu2wZ4jRw7Ytee4a9eusKdNmxZ2zYdew2zZssFesGBB2JcsWQJ7xYoVYdfGy6JFi0ytv3379rCbtWzZMlPLa9u/atUqS2yOKbVq1YK9bt26ptajHW+116R79+6wZ8iQAfYRI0bA3q5dO9gdHR1hL1++POyenp6wv337FvanT5/C3rlzZ9hFRB48eAD77NmzYa9cuTLsP/30E+yZM2eGffny5bBr54VLly7Bni5dOti1886YMWNg184j2vFB+3kTUseOHWEPDg6GferUqbBrr6027rZv3w67dk4uWbIk7NoxRjtuP3z4EPaDBw/C7uLiAnvevHlh/xDt9T158iTsDRs2hP3+/fuwa+dmV1dX2K9duwZ7rly5YPfy8oJdO++MHj0a9s2bN8Ou7VtTpkyBPaG1bt0adu316t27t0UeVzuma5YuXQp7t27dYE+TJg3sX3zxBezaPD82NjYeW/d/mjdvrn5t5cqVsFeqVAn2kJAQ2FOmTAm7dj48ffo07EWKFIH93LlzsGvHS+2cpNHGWMuWLWFv0aKFqfVbQrFixWA/ceIE7NqxWNuvNI8fP4Zdey8gT548sGvX0ho3NzfYDx06BLt2jtFo8w0RfS6VMWNG2LVjuo+PD+zasSZ37tywa+eYiIgI2C9cuAD70aNHYdcUKFAA9itXrphaT0LSri21/UE7ZljKq1evYNeO/9o+oo1Tbfu193+0eYv2HkFoaCjsH1K1alXYtesYbW7k4OBg6nG1MazNT7XrLbPr144PZt+nIf29MG0+rL22t27dgj0oKOjjNswCtPcbNNo5293d3RKb84/Ev5wgIiIiIiIiIiIiIiKr4s0JIiIiIiIiIiIiIiKyKt6cICIiIiIiIiIiIiIiq+LNCSIiIiIiIiIiIiIisirenCAiIiIiIiIiIiIiIquyje+CWbNmhV37xPUaNWrA3qlTp/g+pIiIFC9eHPZChQrBfu/ePdi9vb1hv3v3LuxeXl6wlylTBvYsWbLArn1qu7OzM+wiIm3btoV95syZsG/atAl27RPgzTp48CDs2nYuW7YM9gcPHsDu6OgI+7Vr12Dv2bMn7IlhzJgxsNvY2MAeExMDe5Ik5u4Taq+tj48P7E+fPoX94cOHptafJ08e2K9cuQL7jBkzYN+7dy/s2vMpov9srVu3hn306NHqupDPP/8c9g4dOsCuPUfFihWDvWDBgrDPnj0bdm0fCg8Ph33AgAGwJ4Zt27bB7unpCbt2nM+bNy/svr6+sJ8+fRr2Xr16wV60aFHY9+zZA3vatGlhL126NOzaPmhvbw97kyZNYO/YsSPsIiLNmzeHvUWLFrDfvn0b9mzZssGeO3du2LVzbZEiRWC/ceMG7M2aNYNd258vXboE+6NHj2AvV64c7IlhzZo1ppbX5jknTpyAfdGiRbBrx6Rq1arB3r17d9gHDRoEu7+/P+zaeJkzZw7sXbt2hf3t27ewHz9+HHYRfT/R+jfffAO7dhxOmTIl7OfOnYPdz88Pdu0c2b9/f9h//PFH2DXaa5YpUyZT60loy5cvh71+/foWWX/Tpk1hT548Oez9+vWDPWPGjLBfvnwZ9pCQENi1sXf48GHYs2fPDrs2NpIlSwb7h5QvXx72gIAA2LXrGG2btHno2rVrYQ8ODoZdO2+fPHkSdo32mn1KtGO9dt7X5kDaz+ri4gL78+fPYdfm29p53M7ODnbNwoULYdfm/9q1U65cuWC/evWq+tgFChSAfd68ebAvWbIEdu25084l2jZp50/tuk17n+bWrVuw58+fH/b79+/D/urVK9gTg/YcaHMd7bxvqZ9Jey9syJAhsDs4OMCuvVbjx4+HXZu3R0ZGwh4aGgq7Np8REbG1xW8V7tu3D/bBgwer60K04/nPP/8Me9KkSWHX3s9zd3eH3cPDA/ZUqVLBHh0dDXtsbCzspNPeJ3RycoJde+9Mmye/fPny4zbMAo4cOQJ748aNYdfOC9q19/8C/uUEERERERERERERERFZFW9OEBERERERERERERGRVfHmBBERERERERERERERWRVvThARERERERERERERkVXx5gQREREREREREREREVkVb04QEREREREREREREZFV2cZ3QXd3d9hTp04N++PHj2Hft29ffB9SRESqV68O+7lz52DXtrNFixawX7lyBXbDMGD/9ddfYa9duzbskydPhn3OnDmwi4i0bt0a9vz588MeHh4Oe+HChWG3sbGB/fvvv4d9x44dsGt8fHxgT5s2rant0V4DFxcXU9uTkPz8/GD38vKCffXq1bCHhYXBHhQUBHvTpk1hDwwMhP3y5cuwt2vXDvZjx47BXrduXdhr1aoFu4ODg6nlO3bsCLuISKpUqWD/6aefYHdycoJd29+aNGkC+61bt2DXnmtvb2/Y+/fvD3urVq1gd3R0hP3s2bOwjxkzBvbE8PLlS9iDg4NNrSdlypSwa+OlQIECsBcqVAj2NGnSwK4d8/r27Qv7o0ePYNdERkbC/uzZM9jv3Lmjrmv48OGwDx06FHbtuNq2bVvYly5dCvuwYcNgz5EjB+wlS5aEXdvPM2XKBPuECRNgr1SpEuwHDx6EPTE8f/4cdm0+U7BgQVPrr1atGuxnzpyBfcGCBbBv2rQJdu3cu23bNtjXrVsHe/v27WEfPXo07HZ2drCvWrUKdhF9LqiN1Tdv3qjrQooWLQr71q1bYc+TJw/se/fuhT0mJsbU9syaNQv2LVu2wD5q1CjYu3TpYupxE5o21zlw4ADsT58+hV2be33zzTew+/v7wz5u3DjYixUrBrs2D9eOY2XKlIFdm0vdvXsXdm2eIyKyaNEi2HPmzAl7hQoVYN+zZw/sn3/+Oez37t2DvVevXrBrx8Xx48fDbinaa5wY0qVLB/v+/fth1649tGsA7ZxUqlQp2LW5XZEiRWDXrk+1+bl2Lb1x40bYtXGkHYevXbsGu4hI+vTpYa9SpYr6PYg2p+nevTvshw8fhl0b89o+oc2LtXPPhQsXYLe1xW8NaceyxKDtPydOnIBdOz5r40Lbz7NmzQp70qRJYdeumUNDQ2HXrnk+++wz2B8+fAi7Np8PCAiAXdtnRURu3LgBuzan10RERMCu7c8a7ZyniYqKgj06Ohr2ixcvwq5dL5rd/v8l2jWDdq2uSZIE/y699n6p9rjaPqjt49oxWES/ltauRT80J0O0Y8r/Av7lBBERERERERERERERWRVvThARERERERERERERkVXx5gQREREREREREREREVkVb04QEREREREREREREZFV8eYEERERERERERERERFZlY2hfdz4f6lZsybs+fPnh33ixIkfv1V/EhYWBnvKlClhP3XqFOzXr1+HPTQ0FPZGjRrBnjp1ati1T2HXnl4/Pz/YRURiYmJg1z6tPkWKFLCvXr0a9vHjx8NuZ2cH+4ABA2DftWsX7OXLl4f9t99+g3306NGwa/tQgQIFYE8MBw4cgF17DrT9ZMqUKbA3aNAAdk9Pz7/euD9JkyYN7BMmTIDd19cXdm3c3blzB3ZtX5s7dy7sFy9ehF1EZO3atbBnyJAB9h49esC+ZMkS2KdOnQp7YGAg7PE8dMbp2LEj7Fu3boW9VKlSsGvjqHbt2rAvW7YsHltnWWPHjoW9atWqsD969Aj2w4cPwz5q1KiP27D/kjlzZtgrVaoEe5kyZWC/ceMG7IUKFYK9TZs2sGv7lDZeRPRz8L59+2A/cuQI7Nu3b4e9WLFisGvH/1evXsGeMWNG2LXzWrt27WDXxm/z5s1hv3r1KuwnTpyAPSFpP5O27TVq1IBd20+088vChQthX7x4MewvX76E/bPPPoM9T548sGvzMe18d/nyZdh79+4N+969e2EX0c9hu3fvhj137tywBwcHwz5p0iTYtTmll5cX7Nq5uXr16rAnS5YM9qioKNg1/fr1g33cuHGm1mMp2r7brFkz2LV5snZcCg8Ph71x48awa/ONoKAg2LNlywa7Rnu9tLHRt29f2E+ePAl70aJF1cfWroe01+D+/fuwlytXDnZt7hUdHQ37nDlzYNfmp3369IFdo81bnz17Brv2PMTGxpp6XEvQtkWjHYuvXLkCe8mSJWE/evQo7Nr1oNadnZ1h184x2vWsdi2hjYu3b9/CfvPmTdhFRCIiImBPnjw57C4uLrB7eHjArj3Xz58/h12bu2jzUG2+rMmaNSvs2mvw4sUL2G/dumXqcS1BGxfaezRPnz41tX5tv9WeA23/1N5LcnNzg12bP2vLP3nyBHbtmOfo6Ai7dg0jou8P2lxEewztOR0xYgTsAQEBsO/fvx92S9GuVe7evWtqPWbfI7AEs+eLhNa5c2fYP3RNawmf2vPwMYYPHw77sGHDrLshFhafccG/nCAiIiIiIiIiIiIiIqvizQkiIiIiIiIiIiIiIrIq3pwgIiIiIiIiIiIiIiKr4s0JIiIiIiIiIiIiIiKyKt6cICIiIiIiIiIiIiIiq7KN74ILFiyAPVOmTKYecOjQobDfu3cP9lWrVsGufdp3ixYtYC9evDjsPXv2hD1t2rSwjxkzBvbWrVvDrtmyZYv6tdjYWNiTJMH3krJnzw777NmzYe/WrdtfbN27NmzYAPv48eNh7927N+wVKlSAfenSpbAXLFgQ9okTJ8L+3XffwZ6Q/P39Yb9//z7s2n5rY2MDu6urK+w1atSAvXTp0rBv374d9tq1a8OeOnVq2Bs2bAj7jz/+CPvx48dhd3R0hF17fkREnjx5Anv16tVNrat9+/aw586dG/ZffvkFdu0169ChA+wvXryA/ebNm7CnSpUK9jJlysCeL18+2BPDmTNnYP/+++9hnzNnDuyjR4+GfefOnbD36NED9oEDB8IeEhIC+2+//Qb7smXLYD937hzsGTNmhL1QoUKwjxs3DnYHBwfYRfTjqmbAgAGw58yZE/bp06fDPnz4cNi1cXHhwgXYc+TIAbuLiwvst27dgr1Xr16wnzhxAvbEoJ3rtHN+8uTJYdeeY+2YlzlzZtgXLlwIu3Z+0Z77sLAw2I8dOwb7pEmTYB88eDDsbdu2hf1D5wttvqTNH3x8fGC3tcXT5GHDhsGuzXFbtmwJe/ny5WHX5sQZMmSAXXsutLmm9tonFu1aQrsGMLuew4cPw160aFHY9+/fD/uSJUtg146HmmTJksH+9OlTU+vRtv/69evq9yxevBj2L774AnZtLqKNmcDAQPWxzejTpw/sWbNmhV07Pq1evRp2bX6qzRcSg9lj/ZUrV2BPly4d7NocKGXKlLDXrVsXdm3OV65cOdhTpEgBu6ZWrVqwP3r0CPZdu3bB/tlnn6mPkSdPHtiDg4Nh194nuHr1KuzaPO7ly5fqNiHnz583tbzm+fPnsGvHUG0Olxjs7e1h146fSZMmhV2bY2nXa25ubrC3a9cOdm3+oI3fiIgI2LXxop1HtPXfuXMHdnd3d9hFRDw8PGDXxoX2Mz979gx2bX82ex7RXmNte7Rjq/baZ8mSBfbbt2/HY+v+N3Xq1ClRHlfb/82OC+28KSJiZ2dn6jG0axJt+fDwcPWx/+34lxNERERERERERERERGRVvDlBRERERERERERERERWxZsTRERERERERERERERkVbw5QUREREREREREREREVsWbE0REREREREREREREZFX4I+yB4sWLw37//n1TD5grVy7YK1asCPuWLVtgnzp1Kuw//fQT7DY2NrCXK1cO9tu3b8Peo0cP2JctWwb7yJEjYbe11Z96bVtv3rwJ+6NHj2AvWbIk7N26dYN98uTJsGuvQYoUKWDXtt/V1RX2/Pnzw/748WPY3d3dYU8MNWvWhL1x48awr127FvYqVarA3r59e9h79uwJ+6pVq2AvUKAA7NpzqY2LYsWKwZ48eXLY7e3tYdfGxahRo2AXERk8eDDsWbNmhf3w4cOwnzhxAnZtP584cSLsgwYNgt3X1xf2169fwz5s2DBTy2t27txpavmElDNnTtgHDBgAe9euXWH/4YcfYM+cOTPs2nlKO54bhmFq+S+++AJ2Hx8f2LVjaps2bWDv378/7B+iHQu6dOkC++nTp2Hfvn27qcfV1lO7dm3Yted68+bNsJcuXRr2JUuWwO7n5we7dkzRxm9CmjVrFuyrV6+GXTsGzJ8/H3bt3Lt7927YtfNOv379YF+8eDHs69atg71QoUKwX79+HXZtHvjbb7/BXr9+fdhFRLy9vWEfMmQI7CNGjIC9SZMmsD98+BD2b7/9Fvbs2bPD7uXlBXv69OlhnzJlCuwNGzaEfcOGDbB/aipVqgT78uXLTa3H7DxTO1dp88927drBvm/fPti1n0u7BqhcuTLsLi4usGtjJjg4GHYRkfPnz8Neq1YtU8tr54DAwEDYtfPkN998A7t2nEiWLBns2vlZOzdERkbCrs3rE0Pu3Llh186nV69eNbWeAwcOmFp/dHQ07AULFoT9wYMHsGuv7cCBA2HX9h3t+leb/3/ovH/r1i3YtfNhjRo1YNeuAbT5bNmyZWG3s7ODPSIiAnZPT0/YtfOwdow4dOgQ7Nr1X2LQxm6WLFlg1+b0mhw5csB+48YN2O/cuQO7h4eHqcd9/vw57Np7AU+fPjW1noCAANi1fUdEJCQkBPalS5fCrs3LtPcJvvzyS9h//vln2NOmTQu7NifT3ofIli0b7BcuXID91atXsDs5OcH+v0S79tBeK82zZ89gP3jwIOxz5841tX5t/Gpde59TRB9j2rho3br1X2zduxo0aAC7dg3wb8K/nCAiIiIiIiIiIiIiIqvizQkiIiIiIiIiIiIiIrIq3pwgIiIiIiIiIiIiIiKr4s0JIiIiIiIiIiIiIiKyKt6cICIiIiIiIiIiIiIiq7IxDMOIz4Jjx46FXfsk85cvX8K+fv162I8fPw77iRMnYM+QIQPsGTNmhP2nn36CXdvOx48fw16iRAnYhw8fDnvx4sVhd3Z2hl1EZPHixbCHhITA/vPPP8PesGFD2D09PWEfPHgw7B06dIC9a9eusM+dOxd2Gxsb2GfNmgW79lpu2LAB9iVLlsCekDZt2gT7kydPYJ8wYQLsRYoUgd3X1xf2dOnSwb5o0SLYtWGePHly2L/44gvYf/31V9jDwsJg79atG+zh4eGwFyxYEHYRkZs3b8KujbF9+/bBXqlSJdi150g7Nl28eBH2TJkywV6lShXY69SpA/uWLVtgb9CgAezauIjnIT5RaceG/fv3w16xYkXYtf359evXsB84cAD2ZcuWwd63b1/Yc+fODbufnx/sTZo0gX3SpEmwBwUFwS6ij6UBAwbArp3LkyTBv6tw6tQp2DNnzgx78+bNYY+Ojob9zZs3sGvHgvnz58Ou7UM//vgj7C1atIA9IWnbqJ17Hz58CLv2HEycOBH23r17w64dG7TzTs+ePWFfvnw57NrcxM7ODnbteciaNSvsOXPmhF1ExNHREXZtf9DOzW/fvoU9NDQUdm3+1q5dO9grV64Me6tWrWDXnqPWrVvDrr02S5cuhb1NmzawJ7RcuXLBfv36ddizZ88Ou3asLFSoEOzavEKbA2nHDe35v3r1KuzatYS2v2nr166patSoAbuIyNatW2E/cuQI7NeuXYM9WbJksGvjVdu3YmNjYdecOXMG9vPnz8Nua2sLu7e3N+zadnbv3v2vN87CSpYsCfuxY8dgNzs/1I6T2nlZOweULVsW9ilTpsB+6NAh2DU5cuSAPTg4GHbtNY+MjFQfo0CBArBr+5XZ/VY7/2vdwcEBdu01XrlypantMcvd3R127f2ShFS4cGHY7969C7uPjw/s2jWtm5sb7Nq1rvYekNnz9Y4dO2B3dXWF/UPXBoj2Gn5oXLx48QJ2Jycn2LX37bRzvPbY2vq1+aP2fqQ2VzNLu0bS3qu6ffu2RR7XDO1Ykli0cdGrVy/YZ8+eDfuQIUNg/9B+m1i065I9e/bArl1La9fexYoV+7gN+0TE5z0p/uUEERERERERERERERFZFW9OEBERERERERERERGRVfHmBBERERERERERERERWRVvThARERERERERERERkVXx5gQREREREREREREREVmVjRGfj80WkZIlS8J+9OhR2KtXrw77pUuXYH/58iXsy5Ytg71GjRqw29rawq5t55s3b2AfNWoU7Ddv3oQ9Xbp0sGfNmhX2Fy9ewC4iEhUVBbv2UpUuXRr24cOHm3psZ2dn2IcOHQp7SEgI7IsWLYJdc+fOHdjnzp0Lu/baJAYbGxvYtdfq6dOnsLu7u5t63I4dO8K+YMECU+vRxmO+fPlg3717N+xVq1aF/auvvoK9fv36sN+9exd2ERF7e3vYDx06BLu2n1epUgX2V69ewd61a1fYc+TIAfuQIUNgb9iwIexZsmSBvV27drAHBgbCrh2jx44dC3tCSpo0KewxMTGw79mzB3bttdJ4enrCvm/fPlPLL168GPYOHTqY2h7tONCjRw/Ye/XqBfu8efPUxxgzZgzsSZKY+92DXbt2wV6tWjXYK1WqBLv2XJ89exb2unXrwh4cHAy7pmXLlrCvWLHC1HoSktnzhdn1mDVx4kTY+/XrB/vUqVNh7969O+ytW7eGfeXKlbBHR0fD7u3tDfvp06dhF9Hnjm3btoXdyckJ9vLly8OuHeO6dOkC+6lTp2C/f/8+7NqYHzduHOy//vor7BUqVID9p59+gl2bEyQ07XlOmTIl7FeuXIH96tWrFtsm5LPPPoP9xo0bsGvXJNevX7fYNiEDBw5Uv6bNjTZs2AC7NkcfNGgQ7GnSpIF90qRJsG/cuBF2Hx8f2C0lbdq0sD98+BB2s8dpS3BxcYFdm+9pxwFtTn/x4kVT25M6dWrYtWv4nDlzwq7Nt82e983Snk8RETc3N9hv374N+4gRI2AfMGAA7Nq1sTaH0x73U5MY48LR0RF27Xir7Z+fGu189+zZMytvyV/Trsm180jNmjVht9T1llnae14ODg6wv379GnbtWJYY48JS1wZkeevXr4ddez9Mu5bW5qD/FPEZF/zLCSIiIiIiIiIiIiIisirenCAiIiIiIiIiIiIiIqvizQkiIiIiIiIiIiIiIrIq3pwgIiIiIiIiIiIiIiKr4s0JIiIiIiIiIiIiIiKyKtv4LjhmzBhTK27WrBns7du3hz0qKgr2QoUKwe7n52dqezTFihWDvWnTprD36dMH9hs3bsA+ffp02AMDA9VtWrx4Mey3b9+GPWvWrLDXrVsX9rVr15p6XFdXV9hLly4N+6JFi2Dv2rUr7JkzZ4a9du3asH9KypUrZ2p57TkeN24c7E+fPoV9/PjxsPfs2RP2FClSwH7w4EHYtf25Xr16sGty584N+w8//AC7j4+Puq6wsDDYb926Bfvx48dhz5kzJ+yrVq2CfceOHbDXqFEDdjs7O9irV68Ou3Ysmzx5Muw2Njaw7927F/bEUKlSJVPLf/bZZ7Br+8nmzZthT5YsGexXr16FXdsXYmJiYB8wYADs2vlROwbnzZsX9saNG8P+oeNMmzZtYG/VqhXsy5cvV9eF1K9fH/b79+/Dvm/fPtgHDx4Me0BAAOzaea158+awa8esWrVqwb5t2zbYE9KECRNgb9GiBezaONLG+owZM2DfsGED7NoxT9v/u3fvDvumTZtg184X2njUtqdJkyawa8fCD22TNuZHjBgBu7a/tW3bFnbtWKDNf4YOHQq7dl6rXLky7P3794ddOw8OGzYM9sTi7e0N+8yZM2H38PCAXZtzaOfl8+fPw66d37X5gGbKlCmwa/Nk7ee6cOEC7NmyZYM9bdq06jZpr/26detg1649Xr16Bbs2z9X26fnz58Nu1ty5c2HXxt7Dhw8t8rgJKUuWLLD/+uuvsCdNmhT2169fW2R7tOtB7ZwRGRkJ+507dyyyPU5OTrBXq1YN9pcvX6rrKlGiBOyjR4+G3dfXF3bDMGDXxrA2vrRjovb+gZeXF+zaeVibX2vHSlvbeL9llOC08/jly5dNrUc7Tj5+/Bj22NhY2JMkwb/rmylTJthfvHgB+4f2T0R7TaKjo2FPly4d7M+ePVMfQ/vZ3rx5A7v2nIaHh6uPYYb2npHZY4r2Gmhdo72/QvRnnp6eppZ/9OhRwmzIPwD/coKIiIiIiIiIiIiIiKyKNyeIiIiIiIiIiIiIiMiqeHOCiIiIiIiIiIiIiIisijcniIiIiIiIiIiIiIjIqnhzgoiIiIiIiIiIiIiIrMrGMAzj76xg2rRpsBctWhT2H374AfYtW7bA/vnnn8O+Y8cO2C9evAh7lixZYD927Bjszs7OsA8cONDU+rXnx83NDXYRkalTp8K+fv162P38/GBv27Yt7MmSJYO9Xr16sG/atAl2jfa4M2bMgN3V1RX2kiVLwn706FHY/+au/FF27doF+5QpU2Dfv38/7M2bN4fd398f9po1a8L+yy+/wP7q1SvY58+fD3vq1Klhf/r0KeyzZs2CvX379rAPGzYM9urVq8MuInLjxg3Y8+fPD3vLli1hnz17NuyZM2eGffny5bDb2dnB/vLlS9jv3bsHe9KkSWHXxot2bI2NjYW9WbNmsCekr7/+GvaZM2fCbmNjA7s2po8cOQJ76dKlYZ8+fTrsPXr0gL1Bgwawb9iwAXZtOytXrgy7pm7durB/99136vdo57wzZ87A/vbtW9i18aWdC6Ojo2E/fPgw7IUKFYJ9xIgRsNevXx/2jRs3wn7u3DnYf//9d9g7d+4Me0IqVaoU7Nr+rI2Lbdu2wa6dF7T1jB07FvYBAwbAXqxYMdhPnDgBuzYuypUrB7vm0KFDsD9//lz9HhcXF9h3794Nu3Zu046f2n6o7beaHDlywK6NR83PP/8Me4kSJWB/8OAB7NprnNBy5coFu6enJ+wBAQGwa+N6zZo1sGtzd23MaPu6t7c37IGBgbB7eXnBrl3zaGNVO+8XKFAAdhGR8+fPq19DPvvsM9hr1KgBu/azafPfSZMmmdqehNamTRvYly5dauUt0fdD7RoyLCzM1PodHR1hf/Pmjan1mJUqVSrYtXm1dk1y7do12LV5S9q0adVt0uZSmiZNmsC+evVq2CdOnAi7du7Rrs9CQ0PjsXUfL2fOnLBfv34d9sS49s6QIQPs2n5rdlw4OTnBrl1LW0ry5MlhT5MmDez37983tX5tXvT69Wv1e7Qx+ezZM9g7deoEu3ZNq71fsmjRIti1/T+hx4U2V9BeA+1aKyFp5wtKfGPGjIG9f//+sP/666+wV6tWzWLblBjic77gX04QEREREREREREREZFV8eYEERERERERERERERFZFW9OEBERERERERERERGRVfHmBBERERERERERERERWRVvThARERERERERERERkVXZxnfB8PBw2L/55hvYN27cCHtwcDDs6dKlg33dunV/uW1/ljx5ctjfvHkD+9atW2GfOHEi7Bs2bIB9/PjxsBcoUAD2s2fPwi4ikiQJvmekfdJ7x44dYX/y5Ans5cuXh/3y5cuwb9++HfbatWvDXqJECdi1fUh77vr27Qt7fD7p3VqqVasG+4wZM2CfPHky7I0aNYLd1hYP0QULFsA+d+5c2Lt37w675s6dO7C3bNkS9oULF8JetWpV2D/mNQwJCYF91qxZsFeoUAH2xo0bm3pcbVsrVaoE+/Lly2E/c+YM7KGhobCvWLEC9qJFi8L+9OlT2Js1awZ7QqpVqxbsNjY2sH/77bewR0ZGwv7o0SPYHz9+DLv2GmrnC+2Yqq1HO194enrC3qBBA9hHjBgB+6lTp2AXETl+/DjsW7ZsgT1lypSwa8eOPn36wD5hwgR1m5BLly7Brv3MmzZtgl3bh3bt2gV7586d47F11nHy5EnYf/75Z9i147+fnx/sMTExprbn1atXsFepUgX2X3/9FfY8efLA3qJFC9izZcsGe7FixWAPCgqCfdCgQbB/iDaWbt++DXvatGlhr1evHuxHjx6FvWTJkrA/ePAA9nLlysF+8OBB2O3s7GDPkSMH7MOHD4ddew0S2vXr12HXxm9YWBjs2vPfoUMH2MeNG/fXG/cnpUqVgv38+fOwp0+fHnZt+7XzeJMmTWA/ceKEqe35GHv27IH9+++/h13bp1OnTg27dp0UEREBu7avaFq1agV7QEAA7MuWLYN96dKlph7XElKkSAF74cKFYXdxcYFdO/9qcxTtWK/RjpMPHz6EXZv3atzc3GB/+/Yt7Nr8X7uG/5DMmTPDHhsba3pdiNljkHYNs3btWlPryZ07N+za+P2UmJ3raOdBZ2dn2LX96uLFi6YeN1++fLBfvXoVdkdHR9i1987M0t5f0uaCH/pa0qRJYX/+/Dns9vb2sGvz4lu3bsEeFRUFu3Ysu3fvHuza+E2VKhXs2hyRKD5+++032Nu1awe72eP5vwn/coKIiIiIiIiIiIiIiKyKNyeIiIiIiIiIiIiIiMiqeHOCiIiIiIiIiIiIiIisijcniIiIiIiIiIiIiIjIqnhzgoiIiIiIiIiIiIiIrMrGMAwjPgt+//33sG/evBn2c+fO4Qe0sYnnpn2Y9rglS5aEPU2aNLB7eXnBvm/fPtirV68O+5MnT2AvUaIE7Ddv3oRdRCQwMNBUnz9/PuxRUVGwt2/fHvYzZ87Avm3bNti3bNkC++jRo2E/duwY7NOnT4c9RYoUsN+7dw/2AgUKwJ6Qvv32W9hz5swJe65cuWDfunUr7MHBwbDXr18f9hEjRphaXnsu+/TpA7vmyy+/hL1evXqwOzo6wr5x40b1MbZv3w57lixZYH/27Bns2iFP2w+/+eYbdZuQN2/ewK7t/xUrVoR91apVsO/YsQN2V1dX2KdOnQp7QjJ7nNd+1iNHjsAeHh4Ou7+/P+y9e/eGvXz58rBr+223bt1g14SEhMCunb+01+pD+6DZ51ob20OGDIHd2dkZ9rFjx8KeNGlSU49buXJl2IcOHQq7r68v7Nq4btiwIezr16+HPSFp2/Lo0SPY+/XrB3vdunVh1/arnj17wq7t/9o40rRu3Rr2Tp06wT5nzhxT69eO5T/99JP6PWvWrIF9//79sGvHoHLlysF+8OBB2N3d3WHX5ojjx4+HXRsvgwcPhn3UqFGwv3r1CnYnJyfY43lJYHHacSxZsmSwFypUCPbcuXPDvnLlyo/bsL9pwoQJsGuvb4YMGWB3cXGB/cqVK7CXLl1a3abDhw+rX0sM3t7esGs/w8WLF2GPjIyEXZtHTJw4EfYxY8bA/vTpU9gTktnzuzYffv36NezacUm7Nr58+TLs2vXay5cvYU+SBP9upDbeixYtCru2L2fPnh32oKAg2EVEPD09Yb9z5w7sMTExsGtzcW3eqv3M2jW8RjtXaa+xdg5ImTIl7Nqx5vbt2/HYOsuy1HtJ9vb2sGvHEk2mTJlg164BzNJ+Xu18cffuXVPr186bIiLXrl2DXdtPQkNDYbfUfm6Wh4cH7NrcyNbWFnZtvGvj6OHDh/HYOsuy1LggSijxucbgX04QEREREREREREREZFV8eYEERERERERERERERFZFW9OEBERERERERERERGRVfHmBBERERERERERERERWRVvThARERERERERERERkVXhj6QHxo4dC/vIkSNhv3jxoqkNmTVrFuyZM2eGPU+ePLB7eHiYetzevXvDni5dOtgLFiwI+xdffAH7gQMHYP/888/VbWrcuDHsb968MbVNadOmhT1VqlSwf/nll7C7urrCnj59eti9vLxg37dvH+xr166FXXttZs+eDXuBAgVgT0i+vr6wZ82aFfYiRYrAPnnyZNhdXFxMrUfbdyZMmAD7w4cPYdf2Hc2JEydgd3Nzg13b/oMHD6qPsWLFCtifPXsG+6NHj2AvXrw47Ddu3IB906ZNsNerVw/2a9euwf7999/DniJFCtgXLlwI+++//w77y5cvYU8Mo0ePhj0yMhL2pk2bmupPnz6FvUmTJrDnyJED9qNHj8JuGAbsGrPjqE+fPrCfOXMGdu1YK6KPbW1MasuPHz8edrPPhY2NDexZsmSBfdGiRbBr5ylte06dOgV7tWrVYE8M2vxk/fr1sDdq1Aj2GTNmwH7lyhXYQ0JCYNfO+b/88gvsGnd3d9gXL14M++DBg2HXzuE3b96E/e7du+o2xcbGwn748GH1e5AXL17AXr9+fdibN28O+1dffQV73759YQ8KCoJ97ty5sFesWBH2adOmwf6p+e2332DXjg8BAQGwr1y5EnZbW3y5ox33tLlXx44dYddox3ptnpw7d27YtTGpzc/nzZunblODBg1gv379OuzacUs7v2nLa/O+SZMmwR4YGAh7z549YZ8yZQrs5cqVg127xviUlCpVCvYjR47AHhMTA7u2Pz958gR2bU5jdns02vE5Ojoa9jRp0phaf61atWCfOXOm+j3a+wqhoaGwP3/+HPbw8HDYtevFQ4cOwV6sWDHYtbndh66fEEdHR9i19xrMXhcmpPz588N+4cIF2LV5qXas0uZM2lxcW95StHmvg4ODqfVoc7WrV6+q35M9e3bYtTmK2ceOioqCXTs2ZcqUCXbtNXj9+rWprr1/c+vWLdi1uQURfRz+5QQREREREREREREREVkVb04QEREREREREREREZFV8eYEERERERERERERERFZFW9OEBERERERERERERGRVfHmBBERERERERERERERWZWNYRhGfBZ89uwZ7Hnz5oV94sSJppYvX7487OvXr4e9Zs2asD99+hT21KlTw66ZPXs27K1bt4Z9y5YtsOfPnx/2QoUKqY+9adMm2OvWrat+D1KlShXYs2TJAvvJkydhP3fuHOzR0dGwJ0mC73l98cUXsHt5ecHer18/2DXx3JUtysbGBvbY2FhTy3/zzTewp0+fHnZtHNWvXx927bmZOXMm7N27d4e9Xr16sJ86dQr2H3/8Efb58+fDXqFCBdhFRDp37gy72df9+PHjsE+aNAn2VatWwa69ltqx77vvvoO9VatWsGvP3b1792AfM2YM7DNmzIA9ITVr1gz2HTt2wB4eHg5727ZtYU+ePDnshw8fhj0mJgb28+fPw+7v7w/74MGDYa9Vqxbso0ePhj1Xrlywh4WFwf6hfVzbD+fMmQO7ra0t7GfPnoV9+vTpsHfq1An2hQsXwn7mzBnYtXPh119/Dbv23GnHSu2YZW9vD3tC0s6B2muyYMEC2DNmzAh7SEgI7No+oh17VqxYAbt2LGnTpg3srq6usL948QL2vn37wq7ty+vWrYNdRKRp06awa/OWhg0bwr5hwwbYu3TpAvvRo0dh187NkydPhr1EiRKwZ86cGfbg4GDY8+TJA3tkZCTsixcvhj2haePRw8MD9rt375paf+HChWHXjktmx8bmzZthz5cvH+w5cuSA3cnJCfaCBQvCfuTIEdi9vb1hFxFJmzYt7Nqxu3nz5rD//vvvsE+dOhX2adOmwf7kyRPYtfOhpRQoUAD2N2/ewH79+vWE3BzIzs4O9qioKNgdHR1h134m7Rr1woULsBcrVgz2mzdvwq7NvbTjknb89PT0hF0752nH+YoVK8IuIhIYGAi7r68v7Nq1epEiRWBPmTIl7Hv27IE9Z86csJvdD7X58uvXr2FPkSIF7C9fvoT9U7r2Nru8i4sL7NqcTBtH2nOpyZQpE+za/qy9Jtr54uHDh6a2R9vXRPSxrT13z58/hz1p0qSwa+c2bTxmy5YN9tu3b8P+9u1b2M1ycHCAXXvP69WrVxZ5XDPMjgsia4vP+YJ/OUFERERERERERERERFbFmxNERERERERERERERGRVvDlBRERERERERERERERWxZsTRERERERERERERERkVbw5QUREREREREREREREVmVjxOdjs0Vk8uTJsPfq1QuvWPnEeO3htOWPHDkCe8mSJWHX1KpVC/bff/8d9u7du8PeuXNn2KdOnQp7TEyMqeVFRJo0aQJ7xYoVYQ8KCoLdyckJ9n79+sH+/Plz2NOnTw+7r68v7Pv374e9efPmsM+aNcvU4z569Ah2FxcX2BPSiRMnYLe3t4e9Z8+esP/666+wb9y4EfZNmzbB7ujoCPucOXNgj+fwj/Pw4UPYs2XLBvvr169h18a7s7Oz+tipUqWCvUWLFrBrY+zNmzewa6/NiBEjYJ83bx7s3333Hew7duyAfeXKlbCPHj0a9vbt28Ou7UNmX2NLsLOzgz0qKsrUet6+fQv76dOnYXd1dYXdy8vL1ONOmzYNdm28L1++3NTjzp07F3btmPqh88Xjx49hL1KkCOzbtm2DfcmSJbBr57CtW7fCfvfuXdj79OkD+8yZM2FfvXo17Nr5buHChbBrP5c2fhOSdtzTxrS/vz/sJUqUgF07Z2rni8Si7QtnzpyB/eTJk7A/ffpUfYwcOXLAnjJlSti146T22BptnqMd5zVTpkyBfe/evbBrcwVtDt24cWPYtfGb0LSxYSnaPjdhwgSLrN/d3R32J0+emFqPdt7fvHkz7No1mHYd8SHa/OvFixem12VG0qRJYdfOPdr588KFC7CvW7cO9vv378NeoEAB2M+dOwd7QtLm1sHBwbCnTp0adu1Y2apVK9hXrFgBuzavOHXqFOyafPnywa695jdu3IBdm2tq+7J2DfMh2rV3QECAqfUkSYJ/HzQ2NhZ27ToyMjLS1OP6+fnBfujQIdhDQ0NNrT8xrjES+nxhqeO5pXh7e8MeGBho1e34M7PHGu39CW3/184LyZIlgz08PBx2TZo0aWDX3mPSZMyYEfaQkBBT67GEhB4XRH9XfM4X/MsJIiIiIiIiIiIiIiKyKt6cICIiIiIiIiIiIiIiq+LNCSIiIiIiIiIiIiIisirenCAiIiIiIiIiIiIiIqvizQkiIiIiIiIiIiIiIrIqGyM+H5tNRERERERERERERERkIfzLCSIiIiIiIiIiIiIisirenCAiIiIiIiIiIiIiIqvizQkiIiIiIiIiIiIiIrIq3pwgIiIiIiIiIiIiIiKr4s0JIiIiIiIiIiIiIiKyKt6cICIiIiIiIiIiIiIiq+LNCSIiIiIiIiIiIiIisirenCAiIiIiIiIiIiIiIqvizQkiIiIiIiIiIiIiIrIq3pwgIiIiIiIiIiIiIiKr4s0JIiIiIiIiIiIiIiKyKt6cICIiIiIiIiIiIiIiq7KN74Jz5syBvVu3brB7e3vDHhgYCLuNjQ3s3bt3h33atGmwz507F/bevXvD3q9fP9hLly4Ne9WqVWGvX78+7BUqVIC9Zs2asIuIDB06FHbtZ5gwYQLs69atg90wDNirVasG+4wZM2DPkycP7BovLy/YixUrZmp77O3tYW/atKmp7bGEFStWwL58+XLYO3ToAHuhQoVg154zTYYMGWC/d++eqfVomjRpAnvfvn1hr1SpEuz79u2DPW3atOpjZ86cGXbt2JEqVSrYp0yZAvuuXbtgT506NexLliyBXRu/jx49gj0kJAR2bd/Snuu1a9fCfvPmTdgTkvaa7N69G/bffvsNdu1nTZEihantqVGjBuxVqlSBfdu2bbBfvHgR9ocPH5p63B07dsCeJk0aU+sXEfnyyy9h187ZPXv2hD1Tpkywa+NI29aIiAjYGzZsCLuTkxPsr1+/hl07f2mGDRtmqiekRo0awf7555/D3qJFC9i1/VA7fmrHMG0+o801qlevDnuPHj1gnz59Ouzz58+HXZvXRUdHw96+fXvYRUT69+8Pe+3atWHfunWrui4kNDQUdm1+0rJlS9hnz54Ne9GiRWG/f/8+7Nprlj17dti1892GDRtgT2hmrwFWrVoF++PHj2GfPHky7GFhYbCfPn0a9l9//RX2qKgo2BcuXAh7u3btYNdo8+EbN26Y6olp+PDhsI8YMQL2Tp06wa5d55k1ZswY2AcPHgy7dhxKSNq4qFevHuybNm0ytX5tjhIZGQm7NnfXuLq6wu7o6Aj7gwcPYHdzczPVg4OD/2rT3qOdD8+dOwe7tq2FCxc2tU2enp6wx8TEwH737l3Ynz17BrullC1bFvaDBw8m6OMi2rjQ5kDavFG7LtOupW1t8dtmt2/fhj1JEvw7wNp8++XLl7Br8w2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          },
          "metadata": {}
        }
      ],
      "source": [
        "@torch.no_grad()\n",
        "def sample_with_trajectory(model, schedule, n_samples=1, save_steps=[1000, 800, 600, 400, 200, 100, 50, 0]):\n",
        "    model.eval()\n",
        "\n",
        "    x = torch.randn(n_samples, 1, 28, 28, device=schedule.device)\n",
        "    trajectory = [(1000, x.clone())]\n",
        "\n",
        "    for t in reversed(range(schedule.T)):\n",
        "        t_batch = torch.full((n_samples,), t, device=schedule.device, dtype=torch.float)\n",
        "        epsilon_pred = model(x, t_batch)\n",
        "\n",
        "        alpha_t = schedule.alpha[t]\n",
        "        alpha_bar_t = schedule.alpha_bar[t]\n",
        "        sigma_t = schedule.sigma[t]\n",
        "\n",
        "        z = torch.randn_like(x) if t > 0 else 0\n",
        "        x = (1 / torch.sqrt(alpha_t)) * (x - (1 - alpha_t) / torch.sqrt(1 - alpha_bar_t) * epsilon_pred) + sigma_t * z\n",
        "\n",
        "        if t in save_steps:\n",
        "            trajectory.append((t, x.clone()))\n",
        "\n",
        "    return trajectory\n",
        "\n",
        "# Visualize\n",
        "trajectory = sample_with_trajectory(model, schedule, n_samples=4)\n",
        "\n",
        "fig, axes = plt.subplots(4, len(trajectory), figsize=(2*len(trajectory), 8))\n",
        "for row in range(4):\n",
        "    for col, (t, imgs) in enumerate(trajectory):\n",
        "        img = torch.clamp(imgs[row, 0], -1, 1).cpu().numpy()\n",
        "        img = (img + 1) / 2\n",
        "        axes[row, col].imshow(img, cmap='gray')\n",
        "        axes[row, col].axis('off')\n",
        "        if row == 0:\n",
        "            axes[row, col].set_title(f't={t}')\n",
        "plt.suptitle('Denoising Process', fontsize=16)\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uJE5n7mRplrU"
      },
      "source": [
        "## 8. Save Model"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "id": "eJWL9XKzplrU",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "05a29aac-bf2c-4311-b292-6cb0ccc31567"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model saved to ddpm_mnist.pt\n"
          ]
        }
      ],
      "source": [
        "# Save\n",
        "torch.save(model.state_dict(), 'ddpm_mnist.pt')\n",
        "print(\"Model saved to ddpm_mnist.pt\")\n",
        "\n",
        "# To load later:\n",
        "# model = UNet().to(device)\n",
        "# model.load_state_dict(torch.load('ddpm_mnist.pt'))"
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "8kxOIJoYqSdC"
      },
      "execution_count": null,
      "outputs": []
    }
  ],
  "metadata": {
    "accelerator": "GPU",
    "colab": {
      "gpuType": "A100",
      "provenance": []
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