A Reversible Solver for Diffusion SDEs

Diffusion models have quickly become the state-of-the-art for generation tasks across many different data modalities. An important ability of diffusion models is the ability to encode samples from the data distribution back into the sampling prior distribution. This is useful for performing alterations to real data samples along with guided generation via the continuous adjoint equations. We propose an algebraically reversible solver for diffusion SDEs that can exactly invert real data samples into the prior distribution. Diffusion models have quickly become the state-of-the-art in many different modalities in generation, e.g., audio (Liu et al., 2023), images (Rombach et al., 2022), video (Blattmann et al., 2023), protein generation (Skreta et al., 2024), & c.