Maximum Likelihood Training of Score-Based Diffusion Models

TL;DR

This paper introduces a method to train score-based diffusion models using maximum likelihood, leading to improved likelihood scores and competitive performance on standard datasets.

Contribution

It demonstrates that a specific weighting scheme allows approximate maximum likelihood training of score-based diffusion models, bridging a gap in their training methodology.

Findings

Maximum likelihood training improves model likelihood across datasets.

Achieved state-of-the-art likelihood scores on CIFAR-10 and ImageNet 32x32.

Models perform competitively without data augmentation.

Abstract

Score-based diffusion models synthesize samples by reversing a stochastic process that diffuses data to noise, and are trained by minimizing a weighted combination of score matching losses. The log-likelihood of score-based diffusion models can be tractably computed through a connection to continuous normalizing flows, but log-likelihood is not directly optimized by the weighted combination of score matching losses. We show that for a specific weighting scheme, the objective upper bounds the negative log-likelihood, thus enabling approximate maximum likelihood training of score-based diffusion models. We empirically observe that maximum likelihood training consistently improves the likelihood of score-based diffusion models across multiple datasets, stochastic processes, and model architectures. Our best models achieve negative log-likelihoods of 2.83 and 3.76 bits/dim on CIFAR-10 and ImageNet 32x32 without any data augmentation, on a par with state-of-the-art autoregressive models on these tasks.