Fast Sampling of Diffusion Models via Operator Learning

Diffusion models have found widespread adoption in various areas. However, sampling from them is slow because it involves emulating a reverse process with hundreds-to-thousands of network evaluations. Inspired by the success of neural operators in accelerating differential equations solving, we approach this problem by solving the underlying neural differential equation from an operator learning perspective. We examine probability flow ODE trajectories in diffusion models and observe a compact energy spectrum that can be learned efficiently in Fourier space. With this insight, we propose diffusion Fourier neural operator (DFNO) with temporal convolution in Fourier space to parameterize the operator that maps initial condition to the solution trajectory, which is a continuous function in time. DFNO can be applied to any diffusion model and generate high-quality samples in one model forward call. Our method achieves the state-of-the-art FID of 4.72 on CIFAR-10 using only one model evaluation.