Noise-Adaptive Diffusion Sampling for Inverse Problems Without Task-Specific Tuning

2026-04-18

AI Summary

This work addresses the limitations of existing diffusion models in solving inverse problems, which often suffer from convergence to local optima, overfitting to noise, and deviation from the true data manifold—particularly when the noise type and intensity are unknown. The authors propose Noise-space Hamiltonian Monte Carlo (N-HMC), which reformulates reverse diffusion as a deterministic mapping from initial noise to a clean image and performs posterior sampling in the noise space to effectively explore the solution space while preserving manifold consistency. Furthermore, they introduce a noise-adaptive mechanism (NA-NHMC) that robustly handles diverse inverse problems without requiring prior knowledge of noise characteristics or task-specific hyperparameter tuning. Experiments demonstrate that the proposed method significantly outperforms current approaches across four linear and three nonlinear inverse problems, achieving high reconstruction quality and exhibiting strong robustness to hyperparameters and initialization.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Diffusion models (DMs) have recently shown remarkable performance on inverse problems (IPs). Optimization-based methods can fast solve IPs using DMs as powerful regularizers, but they are susceptible to local minima and noise overfitting. Although DMs can provide strong priors for Bayesian approaches, enforcing measurement consistency during the denoising process leads to manifold infeasibility issues. We propose Noise-space Hamiltonian Monte Carlo (N-HMC), a posterior sampling method that treats reverse diffusion as a deterministic mapping from initial noise to clean images. N-HMC enables comprehensive exploration of the solution space, avoiding local optima. By moving inference entirely into the initial-noise space, N-HMC keeps proposals on the learned data manifold. We provide a comprehensive theoretical analysis of our approach and extend the framework to a noise-adaptive variant (NA-NHMC) that effectively handles IPs with unknown noise type and level. Extensive experiments across four linear and three nonlinear inverse problems demonstrate that NA-NHMC achieves superior reconstruction quality with robust performance across different hyperparameters and initializations, significantly outperforming recent state-of-the-art methods. The code is available at https://github.com/NA-HMC/NA-HMC.

Problem

• inverse problems
• diffusion models
• noise adaptation
• manifold infeasibility
• posterior sampling

Innovation

• Noise-space Hamiltonian Monte Carlo
• Diffusion Models
• Inverse Problems
• Noise-Adaptive Sampling
• Manifold Consistency