Neural Diffusion Models
This work addresses a bottleneck in generative modeling for researchers and practitioners by generalizing diffusion models to allow more flexible transformations, though it appears incremental as it builds directly on existing diffusion frameworks.
The paper tackles the limitation of conventional diffusion models being restricted to linear transformations by introducing Neural Diffusion Models (NDMs), which enable time-dependent non-linear transformations, resulting in improved likelihood and high-quality sample generation on benchmarks like CIFAR-10 and ImageNet.
Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of transformations can potentially help train generative distributions more efficiently, simplifying the reverse process and closing the gap between the true negative log-likelihood and the variational approximation. In this paper, we present Neural Diffusion Models (NDMs), a generalization of conventional diffusion models that enables defining and learning time-dependent non-linear transformations of data. We show how to optimise NDMs using a variational bound in a simulation-free setting. Moreover, we derive a time-continuous formulation of NDMs, which allows fast and reliable inference using off-the-shelf numerical ODE and SDE solvers. Finally, we demonstrate the utility of NDMs with learnable transformations through experiments on standard image generation benchmarks, including CIFAR-10, downsampled versions of ImageNet and CelebA-HQ. NDMs outperform conventional diffusion models in terms of likelihood and produce high-quality samples.