{ "source_file": "0930", "source_platform": "Medium", "author": "Aqeel Anwar", "title_listed": "Difference between AutoEncoder (AE) and Variational AutoEncoder (VAE)", "keywords": "AutoEncoder,VAE", "domain": "机器学习", "content_type": "深度技术解析", "is_paid_flag": "部分免费/会员墙", "url": "https://towardsdatascience.com/difference-between-autoencoder-ae-and-variational-autoencoder-vae-ed7be1c038f2/", "publish_date": "2021-11", "corpus_stage": "预训练/SFT", "notes": "", "id": "2c791ce76bf9", "collected_at": "2026-10-01T23:11:02", "title": "Difference between AutoEncoder (AE) and Variational AutoEncoder (VAE) | Towards Data Science", "body_markdown": "![Revisit consent button](https://cdn-cookieyes.com/assets/images/revisit.svg)\nWe value your privacy\nWe use cookies to enhance your browsing experience, serve personalised ads or content, and analyse our traffic. 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That is what Autoencoder and Variational Autoencoder are.\n[Aqeel Anwar](https://towardsdatascience.com/author/aqeel%20anwar/)\nNovember 3, 20218 min read\n> The ability to simplify means to eliminate the unnecessary so that the necessary may speak — **Hans Hofmann**\n# Context— Data compression\nData compression is an essential phase in training a network. The idea is to compress the data so that the same amount of information can be represented by fewer bits. This also helps with the problem of the curse of dimensionality. A dataset with many attributes is different to train with because it tends to overfit the model. Hence dimensionality reduction techniques need to be applied before the dataset can be used for training.\nThis is where the Autoencoder (AE) and Variational Autoencoder (VAE) come into play. They are end-to-end networks that are used to compress the input data. Both Autoencoder and Variational Autoencoder are used to transform the data from a higher to lower-dimensional space, essentially achieving compression.\n# Autoencoder — AE\n## What is it?\nAutoencoder is used to learn efficient embeddings of unlabeled data for a given network configuration. The autoencoder consists of two parts, an encoder, and a decoder. The encoder compresses the data from a higher-dimensional space to a lower-dimensional space (also called the latent space), while the decoder does the opposite i.e., convert the latent space back to higher-dimensional space. The decoder is used to ensure that latent space can capture most of the information from the dataset space, by forcing it to output what was fed as input to the decoder.\n## Block Diagram\nThe block diagram can be seen below.\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2025/03/image-114.png)\nAutoEncoder — Image by Author\nDuring training, the input data x is fed to the encoder function _**e_theta(x)**_. The input is passed through a series of layers (parameterized by the variable theta) reducing its dimensions to achieve a compressed latent vector _**z**_. The number of layers, type and size of the layers, and the latent space dimension are user-controlled parameters. Compression is achieved if the dimension of the latent space is less than that of the input space, essentially getting rid of redundant attributes.\nThe decoder _**d_phi(z)**_ usually (but not necessarily) consists of near-compliment layers of the layers used in the encoder but in reverse order. A near-complement layer of a layer is the one that can be used to undo the operations (to some extent) of the original layer such as transposed conv layer to conv layer, pooling to unpooling, fully connected to fully connected, etc.\n## Loss function\nThe entire encoder-decoder architecture is collectively trained on the loss function which encourages that the input is reconstructed at the output. Hence the loss function is the mean squared error between the encoder input and the decoder output.\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2025/03/image-115.png)\nAutoencoder loss function — Image by Author\nThe idea is to have a very low dimensional latent space so that maximum compression is achieved, but at the same time, the error is small enough. Reducing the dimension of the latent space beyond a certain value will result in a significant loss of information.\nThere are no constraints on the values/distribution of the latent space. It can be anything, as long as it can reconstruct the input when the decoder function is applied to it.\n## Latent space visualization\nBelow is an example of the latent space generated by training the network on an MNIST dataset.\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2025/03/image-116.png)\nLatent space of Autoencoder — Image by Author\nIt can be seen that the same digits tend to cluster themselves in the latent space. Another important thing to note is that there are parts of the latent space that doesn't correspond to any data point. Using those as inputs to the encoder will result in an output that doesn’t look like any digit from the MNIST data. This is what we mean by that the latent space is not regularized. Such a latent space only has a few regions/cluster that has the generative capability, which means that sampling any point in the latent space that belongs within a cluster will generate a variation of the data that the cluster belongs to. But the entire latent space does not have the generative capability. The regions which do not belong to any cluster will generate garbage output. Once the network is trained, and the training data is removed, we have no way of knowing if the output generated by the decoder from a randomly sampled latent vector is valid or not. Hence AE is mainly used for compression.\n> For valid inputs, the AE is able to compress them to fewer bits essentially getting rid of the redundancy (Encoder) but due to non-regularized latent space AE, the decoder can not be used to generate valid input data from latent from vectors sampled from the latent space.\n## Why use AE for compression?\nThe latent space of a linear autoencoder strongly resembles the eigenspace achieved during the principal component analysis of the data. A linear autoencoder with input space dimension _**n**_ and latent space dimensions set to _**m