Entropy-aware Variance Optimization for Diffusion Inference
Shigui Li, Wei Chen, Delu Zeng
Diffusion models (DMs) excel in image generation, but suffer from slow inference and training-inference discrepancies. Although gradient-based solvers like DPM-Solver accelerate sampling inference of DMs, they lack theoretical foundations in information transmission efficiency. This paper introduces an information-theoretic perspective on the diffusion inference processes, revealing that successful denoising fundamentally reduces conditional entropy during reverse transitions. This principle leads to two key insights: (1) data prediction parameterization outperforms its noise counterpart in entropy reduction, and (2) conditional variance optimization that minimizes transition and reconstruction errors through conditional entropy reduction. Building on these insights, we propose entropy-aware variance optimization for diffusion inference, called *EvoDiff*, that systematically reduces uncertainty during denoising by optimizing conditional entropy reduction. Extensive experiments on DMs validate our insights and demonstrate that the proposed method consistently outperforms state-of-the-art gradient-based solvers. For example, compared to the baseline method, EvoDiff reduces reconstruction error by up to 45.5\%  (FID from 5.10 to 2.78) at 10 function evaluations (NFE) on CIFAR-10, cuts function evaluation cost by 25\% (from 20 to 15 NFE) for high-quality samples on ImageNet-256, and improves text-to-image generation while reducing artifacts.