Filtered Posterior Mean Collections: A Unified Framework for Analytical Models of Diffusion Generalization

2026-05-22

AI Summary

Existing image diffusion models lack a unified analytical framework for modeling the generalization behavior of neural denoising functions. This work proposes the Filtered Posterior Mean Collections (FPMCs) framework, which, for the first time, unifies various posterior-weighted averaging methods based on training data patches into a single formalism. FPMCs systematically integrates and generalizes these approaches along three design axes: query precision vectors, response weights, and source distributions. To further enhance performance, the framework introduces soft relaxation and source distribution augmentation strategies. Experimental results demonstrate that FPMCs consistently and significantly improve sample quality across three natural image datasets, confirming its effectiveness and broad applicability.

Abstract

The neural-network denoising functions which form the backbone of image diffusion models are remarkably consistent in their generalization behaviour across a wide variety of network architectures and training procedure hyperparameters. A recent line of research has sought to model the outputs of these networks by aggregating posterior weighted averages of training dataset patches. In this work, we consolidate these approaches into a unified model class which we call Filtered Posterior Mean Collections (FPMCs). We define this model class using query precision vectors, response weights, and source distributions, and illustrate that existing methods are recoverable with specific choices of these design axes. Investigating each axis in turn, we find that FPMC performance can be improved with soft relaxations of prior patch-based methods, and through augmentations of source distributions. Applying these findings to an existing FPMC, we demonstrate consistent sample improvement across three natural image datasets.

Problem

• diffusion models
• posterior mean
• generalization
• denoising functions
• image generation

Innovation

• Filtered Posterior Mean Collections
• diffusion models
• posterior aggregation
• generalization
• source distribution augmentation