Mixture-of-Gaussians-Guided Schedule Design for Brownian Bridge Diffusion Models

2026-07-03

AI Summary

This work addresses the lack of systematic design in bridging schedules for Brownian Bridge diffusion models, where existing approaches predominantly rely on heuristic choices. By adopting a Gaussian mixture prior, the authors analytically derive the optimal posterior and the corresponding MMSE denoiser for the reverse process, establishing an interpretable reconstruction principle. They further propose a scheduling framework that jointly optimizes perceptual quality—measured by the Wasserstein criterion—and reconstruction fidelity—quantified by the MSE criterion—revealing an inherent trade-off between the two. Notably, they prove the existence of a universal scheduling strategy independent of both the degradation type and the prior distribution. Theoretical findings are fully validated in controlled Gaussian mixture experiments and demonstrate significant performance gains over state-of-the-art methods on FFHQ image inpainting, deblurring, and super-resolution tasks.

Abstract

Brownian Bridge Diffusion Models (BBDM) offer an appealing framework for image restoration and inverse problems by constructing a stochastic bridge from the clean signal directly to the degraded observation, rather than to pure noise. Despite their promise, the choice of bridge schedule is typically inherited from heuristics, and a principled analytical framework for schedule design has been lacking. In this work, we develop such a framework by offering a novel analysis of BBDM reverse dynamics under a Mixture-of-Gaussians (MoG) prior. This setting yields a closed-form ideal posterior and a corresponding MMSE denoiser, while the BBDM-induced reconstruction law is captured analytically through a tractable surrogate. Building on these expressions, we formulate two complementary schedule-design objectives: a Wasserstein criterion targeting perceptual quality and an MSE criterion targeting reconstruction fidelity. Our work exposes an inherent tradeoff between the two and proves the existence of universal schedules for both that are independent of the degradation and prior. Extensive experiments on controlled MoG settings confirm full alignment between theory and practice, and experiments on the FFHQ dataset across inpainting, deblurring, and super-resolution tasks validate the practical value of our schedule-design criteria.

Problem

• Brownian Bridge Diffusion Models
• schedule design
• Mixture-of-Gaussians prior
• image restoration
• inverse problems

Innovation

• Mixture-of-Gaussians
• Brownian Bridge Diffusion Models
• schedule design
• MMSE denoiser
• Wasserstein criterion