Measurement Score-Based Diffusion Model

2025-05-17

AI Summary

Training diffusion models without clean ground-truth images remains challenging. To address this, this paper proposes the Measurement Score Modeling (MSM) framework, which learns partial measurement scores directly from noisy, undersampled measurements—without requiring any clean image supervision. Its core contributions are: (1) a theoretical characterization of the biased score expectation induced by stochastic subsampling; and (2) a provably convergent stochastic sampling and posterior reconstruction algorithm, grounded in variational inference and KL-divergence analysis. Evaluated on natural image generation and multi-coil MRI reconstruction, MSM achieves high-fidelity image synthesis and effective inverse problem solving—even when no clean training data is available. This significantly broadens the applicability of diffusion models to realistic, resource-constrained observation settings. The implementation is publicly available.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Large Multimodal Models (LMMs)
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Web Mining and Content Analysis: Large pretrained models with web data
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Diffusion models are widely used in applications ranging from image generation to inverse problems. However, training diffusion models typically requires clean ground-truth images, which are unavailable in many applications. We introduce the Measurement Score-based diffusion Model (MSM), a novel framework that learns partial measurement scores using only noisy and subsampled measurements. MSM models the distribution of full measurements as an expectation over partial scores induced by randomized subsampling. To make the MSM representation computationally efficient, we also develop a stochastic sampling algorithm that generates full images by using a randomly selected subset of partial scores at each step. We additionally propose a new posterior sampling method for solving inverse problems that reconstructs images using these partial scores. We provide a theoretical analysis that bounds the Kullback-Leibler divergence between the distributions induced by full and stochastic sampling, establishing the accuracy of the proposed algorithm. We demonstrate the effectiveness of MSM on natural images and multi-coil MRI, showing that it can generate high-quality images and solve inverse problems -- all without access to clean training data. Code is available at https://github.com/wustl-cig/MSM.

Problem

• Develops diffusion model using noisy measurements
• Efficient sampling with partial measurement scores
• Solves inverse problems without clean data

Innovation

• Uses partial measurement scores from noisy data
• Stochastic sampling with randomized subset selection
• Novel posterior sampling for inverse problems