On Density Estimation with Diffusion Models

We introduce a flexible family of diffusion-based generative models that achieves state-of-the-art likelihoods on image density estimation benchmarks. Unlike other diffusion-based models, our method allows for efficient optimization of the noise schedule jointly with the rest of the model. We show that the evidence lower bound (ELBO) for our model simplifies to a remarkably short expression in terms of the signal-to-noise ratio of the diffusion process, thereby improving our theoretical understanding of this model class. Using this insight, we prove an equivalence between several models proposed in the literature. In addition, we show that the continuous-time ELBO is invariant to the noise schedule, except for the signal-tonoise ratio at its endpoints. This enables us to learn a noise schedule that minimizes the variance of the resulting ELBO estimator, leading to faster optimization. Combining these advances with architectural improvements, we obtain state-of-the-art likelihoods on the CIFAR-10 and ImageNet density estimation benchmarks, outperforming autoregressive models that have dominated these benchmarks for many years.