# Particle-Filtering-based Latent Diffusion for Inverse Problems

arXiv: https://arxiv.org/abs/2408.13868 · HTML: https://mlsanity.com/paper/2408.13868/

## Key facts

- Cited by 5 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 23 of its 47 references that are in the map.
- First posted on arXiv 25 Aug 2024.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [A Survey on Generative Diffusion Model](https://mlsanity.com/paper/2209.02646/) (2022)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models](https://mlsanity.com/paper/2307.00619/) (2023)
- [Diffusion with Forward Models: Solving Stochastic Inverse Problems Without Direct Supervision](https://mlsanity.com/paper/2306.11719/) (2023)
- [Adversarial Regularizers in Inverse Problems](https://mlsanity.com/paper/1805.11572/) (2018)
- [Soft Diffusion: Score Matching for General Corruptions](https://mlsanity.com/paper/2209.05442/) (2022)
- [Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion](https://mlsanity.com/paper/2312.00852/) (2023)
- [Prompt-tuning latent diffusion models for inverse problems](https://mlsanity.com/paper/2310.01110/) (2023)
- [Solving Linear Inverse Problems Using GAN Priors: An Algorithm with Provable Guarantees](https://mlsanity.com/paper/1802.08406/) (2018)
- [On Analyzing Generative and Denoising Capabilities of Diffusion-based Deep Generative Models](https://mlsanity.com/paper/2206.00070/) (2022)
- [Learning Image Priors through Patch-based Diffusion Models for Solving Inverse Problems](https://mlsanity.com/paper/2406.02462/) (2024)
- [Deep Convolutional Likelihood Particle Filter for Visual Tracking](https://mlsanity.com/paper/2006.06746/) (2020)

## Built on by (most cited first, 5 of 5)

- [Inverse Problem Sampling in Latent Space Using Sequential Monte Carlo](https://mlsanity.com/paper/2502.05908/) (2025)
- [Inference-Time Scaling of Diffusion Language Models via Trajectory Refinement](https://mlsanity.com/paper/2507.08390/) (2025)
- [Kernel Density Steering: Inference-Time Scaling via Mode Seeking for Image Restoration](https://mlsanity.com/paper/2507.05604/) (2025)
- [On the Relation of State Space Models and Hidden Markov Models](https://mlsanity.com/paper/2601.13357/) (2026)
- [Non-Asymptotic Error Bounds for SMC with Biased Proposals: Application to Conditional Diffusion Sampling](https://mlsanity.com/paper/2607.04780/) (2026)

## Abstract (arXiv)

Current strategies for solving image-based inverse problems apply latent diffusion models to perform posterior sampling.However, almost all approaches make no explicit attempt to explore the solution space, instead drawing only a single sample from a Gaussian distribution from which to generate their solution. In this paper, we introduce a particle-filtering-based framework for a nonlinear exploration of the solution space in the initial stages of reverse SDE methods. Our proposed particle-filtering-based latent diffusion (PFLD) method and proposed problem formulation and framework can be applied to any diffusion-based solution for linear or nonlinear inverse problems. Our experimental results show that PFLD outperforms the SoTA solver PSLD on the FFHQ-1K and ImageNet-1K datasets on inverse problem tasks of super resolution, Gaussian debluring and inpainting.