mlsanityData to 7 Oct 2026

MADE: Masked Autoencoder for Distribution Estimation

arXiv 1502.03509 ↗First posted 12 Feb 2015cs.LG cs.NE stat.MLcited by 306

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Cited by 20 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

There has been a lot of recent interest in designing neural network models to estimate a distribution from a set of examples. We introduce a simple modification for autoencoder neural networks that yields powerful generative models. Our method masks the autoencoder's parameters to respect autoregressive constraints: each input is reconstructed only from previous inputs in a given ordering. Constrained this way, the autoencoder outputs can be interpreted as a set of conditional probabilities, and their product, the full joint probability. We can also train a single network that can decompose the joint probability in multiple different orderings. Our simple framework can be applied to multiple architectures, including deep ones. Vectorized implementations, such as on GPUs, are simple and fast. Experiments demonstrate that this approach is competitive with state-of-the-art tractable distribution estimators. At test time, the method is significantly faster and scales better than other autoregressive estimators.

Key facts. Cited by 306 papers in the map (data through 7 Oct 2026). First posted on arXiv 12 Feb 2015.

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Citing papers per year: 2019: 1; 2020: 0; 2021: 68; 2022: 55; 2023: 67; 2024: 45; 2025: 42; 2026: 28.

306 papers.

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38 more
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