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

arXiv: https://arxiv.org/abs/2603.01837 · HTML: https://mlsanity.com/paper/2603.01837/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 25 of its 46 references that are in the map.
- First posted on arXiv 2 Mar 2026.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 25 of 25)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [PULSE: Self-Supervised Photo Upsampling via Latent Space Exploration of Generative Models](https://mlsanity.com/paper/2003.03808/) (2020)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [Path Integral Sampler: a stochastic control approach for sampling](https://mlsanity.com/paper/2111.15141/) (2021)
- [Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing](https://mlsanity.com/paper/2407.01521/) (2024)
- [Restart Sampling for Improving Generative Processes](https://mlsanity.com/paper/2306.14878/) (2023)
- [A Review of Convolutional Neural Networks for Inverse Problems in Imaging](https://mlsanity.com/paper/1710.04011/) (2017)
- [SA-Solver: Stochastic Adams Solver for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2309.05019/) (2023)
- [InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciences](https://mlsanity.com/paper/2503.11043/) (2025)
- [Quantization Guided JPEG Artifact Correction](https://mlsanity.com/paper/2004.09320/) (2020)
- [Symbolic Music Generation with Non-Differentiable Rule Guided Diffusion](https://mlsanity.com/paper/2402.14285/) (2024)
- [Provable Probabilistic Imaging using Score-Based Generative Priors](https://mlsanity.com/paper/2310.10835/) (2023)
- [JPEG Artifact Correction using Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2209.11888/) (2022)
- [Vec2Face: Unveil Human Faces from their Blackbox Features in Face Recognition](https://mlsanity.com/paper/2003.06958/) (2020)
- [Accelerating Diffusion Models for Inverse Problems through Shortcut Sampling](https://mlsanity.com/paper/2305.16965/) (2023)
- [Ensemble Kalman Diffusion Guidance: A Derivative-free Method for Inverse Problems](https://mlsanity.com/paper/2409.20175/) (2024)
- [Solving General Noisy Inverse Problem via Posterior Sampling: A Policy Gradient Viewpoint](https://mlsanity.com/paper/2403.10585/) (2024)

## Built on by (most cited first, 1 of 1)

- [Training-free Controllable Human Motion Generation under Heterogeneous Constraints](https://mlsanity.com/paper/2607.01990/) (2026)

## Abstract (arXiv)

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 textbfConstrained 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.