New Covariance-Aware Sampler Boosts Few-Step Diffusion Model Quality

Diffusion models typically rely on predicting the mean of the reverse distribution during sampling, but this approach fails in the few-step regime because it ignores the covariance. Schioppa and Salimans (2026) address this gap with a covariance-aware sampler that explicitly estimates the reverse-process covariance using Tweedie's formula. They decompose the covariance matrix efficiently in Fourier space, allowing the method to be implemented as a lightweight extension of DDIM. The overhead is minimal — just one additional Jacobian-Vector Product per sampling step — making it practical for real-world use.

In experiments on pixel-based diffusion models, the proposed sampler consistently produces higher-quality samples than current second-order samplers like Heun and DPM-Solver++, as well as the recent aDDIM sampler, all at the same number of function evaluations. This improvement is especially pronounced at very few steps, where traditional methods suffer from quality degradation. The work provides a principled way to enhance diffusion model sampling without increasing compute budget, potentially accelerating applications in image generation and editing.