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arXiv · 2402.10095

Classification Diffusion Models: Revitalizing Density Ratio Estimation

Shahar Yadin·Noam Elata·Tomer Michaeli
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Abstract

A prominent family of methods for learning data distributions relies on density ratio estimation (DRE), where a model is trained to $\textit{classify}$ between data samples and samples from some reference distribution. DRE-based models can directly output the likelihood for any given input, a highly desired property that is lacking in most generative techniques. Nevertheless, to date, DRE methods have failed in accurately capturing the distributions of complex high-dimensional data, like images, and have thus been drawing reduced research attention in recent years. In this work we present $\textit{classification diffusion models}$ (CDMs), a DRE-based generative method that adopts the formalism of denoising diffusion models (DDMs) while making use of a classifier that predicts the level of noise added to a clean signal. Our method is based on an analytical connection that we derive between the MSE-optimal denoiser for removing white Gaussian noise and the cross-entropy-optimal classifier for predicting the noise level. Our method is the first DRE-based technique that can successfully generate images beyond the MNIST dataset. Furthermore, it can output the likelihood of any input in a single forward pass, achieving state-of-the-art negative log likelihood (NLL) among methods with this property. Code is available on the project's webpage in https://shaharYadin.github.io/CDM/ .

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Shahar Yadin, Noam Elata, Tomer Michaeli. 2024-10-31. Classification Diffusion Models: Revitalizing Density Ratio Estimation. https://arxiv.org/abs/2402.10095

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