# Interacting particle guidance for sampling reward-tilted generative priors

arXiv: https://arxiv.org/abs/2609.37227 · HTML: https://mlsanity.com/paper/2609.37227/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 45 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 30 of 34)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [A General Framework for Inference-time Scaling and Steering of Diffusion Models](https://mlsanity.com/paper/2501.06848/) (2025)
- [Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts](https://mlsanity.com/paper/2503.02819/) (2025)
- [Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2102.07501/) (2021)
- [Training-free Linear Image Inverses via Flows](https://mlsanity.com/paper/2310.04432/) (2023)
- [Amortizing intractable inference in diffusion models for vision, language, and control](https://mlsanity.com/paper/2405.20971/) (2024)
- [NETS: A Non-Equilibrium Transport Sampler](https://mlsanity.com/paper/2410.02711/) (2024)
- [FlowDPS: Flow-Driven Posterior Sampling for Inverse Problems](https://mlsanity.com/paper/2503.08136/) (2025)
- [Proteina: Scaling Flow-based Protein Structure Generative Models](https://mlsanity.com/paper/2503.00710/) (2025)
- [Elements of Sequential Monte Carlo](https://mlsanity.com/paper/1903.04797/) (2019)
- [Control functionals for Monte Carlo integration](https://mlsanity.com/paper/1410.2392/) (2014)
- [Meta Flow Maps enable scalable reward alignment](https://mlsanity.com/paper/2601.14430/) (2026)
- [Diamond Maps: Efficient Reward Alignment via Stochastic Flow Maps](https://mlsanity.com/paper/2602.05993/) (2026)
- [Sampling in Unit Time with Kernel Fisher-Rao Flow](https://mlsanity.com/paper/2401.03892/) (2024)
- [DriftLite: Lightweight Drift Control for Inference-Time Scaling of Diffusion Models](https://mlsanity.com/paper/2509.21655/) (2025)
- [Tilt Matching for Scalable Sampling and Fine-Tuning](https://mlsanity.com/paper/2512.21829/) (2025)
- [Deep MMD Gradient Flow without adversarial training](https://mlsanity.com/paper/2405.06780/) (2024)
- [Stochastic Gradient MCMC with Repulsive Forces](https://mlsanity.com/paper/1812.00071/) (2018)
- [Stein Variational Gradient Descent: many-particle and long-time asymptotics](https://mlsanity.com/paper/2102.12956/) (2021)
- [Source-Guided Flow Matching](https://mlsanity.com/paper/2508.14807/) (2025)
- [Stein transport for Bayesian inference](https://mlsanity.com/paper/2409.01464/) (2024)
- [Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlo](https://mlsanity.com/paper/2502.06379/) (2025)

## Abstract (arXiv)

Inference-time steering adapts pretrained diffusion and flow-based models to new tasks, e.g., to generate samples from a conditional distribution or samples with desired properties, without retraining. This can be formalized as sampling from a reward-tilted generative prior. As exact sampling from this distribution is intractable, guidance-based methods rely on approximations producing biased samples, and sequential Monte Carlo (SMC) methods correct for this bias using importance weights. However, while exact in the large particle limit, SMC suffers from weight degeneracy and particle collapse in practice. We propose interacting particle guidance (IPG), which replaces reweighting with transport. The particles interact through an additional drift, derived from the Feynman--Kac PDE to cancel the reweighting term, and remain unweighted. Choosing the drift in a reproducing kernel Hilbert space yields a closed-form solution that is cheap to compute, with negligible overhead compared to SMC. We demonstrate the method on Gaussian mixtures with known posteriors, and on high-dimensional image inpainting and protein structure inference tasks.