Constrained Particle Seeking: Solving Diffusion Inverse Problems with Just Forward Passes

TL;DR

Constrained Particle Seeking (CPS) is a gradient-free method for inverse problems that actively searches for optimal solutions using particle information and constraints, matching gradient-based methods' performance.

Contribution

CPS introduces a novel gradient-free, constrained optimization approach for inverse problems, enabling flexible and efficient particle seeking without requiring gradient information.

Findings

Effective in image and scientific inverse problems

Achieves comparable results to gradient-based methods

Outperforms other gradient-free approaches

Abstract

Diffusion models have gained prominence as powerful generative tools for solving inverse problems due to their ability to model complex data distributions. However, existing methods typically rely on complete knowledge of the forward observation process to compute gradients for guided sampling, limiting their applicability in scenarios where such information is unavailable. In this work, we introduce \textbf{\emph{Constrained Particle Seeking (CPS)}}, a novel gradient-free approach that leverages all candidate particle information to actively search for the optimal particle while incorporating constraints aligned with high-density regions of the unconditional prior. Unlike previous methods that passively select promising candidates, CPS reformulates the inverse problem as a constrained optimization task, enabling more flexible and efficient particle seeking. We demonstrate that CPS can effectively solve both image and scientific inverse problems, achieving results comparable to gradient-based methods while significantly outperforming gradient-free alternatives. Code is available at https://github.com/deng-ai-lab/CPS.