# CREPE: Controlling Diffusion with Replica Exchange

arXiv: https://arxiv.org/abs/2509.23265 · HTML: https://mlsanity.com/paper/2509.23265/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 48 of its 81 references that are in the map.
- First posted on arXiv 27 Sep 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 48)

- [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)
- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [OGBench: Benchmarking Offline Goal-Conditioned RL](https://mlsanity.com/paper/2410.20092/) (2024)
- [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)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decoding](https://mlsanity.com/paper/2408.08252/) (2024)
- [Iterated Denoising Energy Matching for Sampling from Boltzmann Densities](https://mlsanity.com/paper/2402.06121/) (2024)
- [TFG: Unified Training-Free Guidance for Diffusion Models](https://mlsanity.com/paper/2409.15761/) (2024)
- [Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts](https://mlsanity.com/paper/2503.02819/) (2025)
- [Beyond ELBOs: A Large-Scale Evaluation of Variational Methods for Sampling](https://mlsanity.com/paper/2406.07423/) (2024)
- [OpenMM 8: Molecular Dynamics Simulation with Machine Learning Potentials](https://mlsanity.com/paper/2310.03121/) (2023)
- [DEFT: Efficient Fine-Tuning of Diffusion Models by Learning the Generalised h-transform](https://mlsanity.com/paper/2406.01781/) (2024)

## Built on by (most cited first, 11 of 11)

- [SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogate](https://mlsanity.com/paper/2605.18745/) (2026)
- [Towards Diverse Scientific Hypothesis Search with Large Language Models](https://mlsanity.com/paper/2606.10587/) (2026)
- [Diffusion Alignment Beyond KL: Variance Minimisation as Effective Policy Optimiser](https://mlsanity.com/paper/2602.12229/) (2026)
- [Composing diffusion priors with explicit physical context via generative Gibbs sampling](https://mlsanity.com/paper/2605.10642/) (2026)
- [Recipes for Steering and Scaling LLMs via Sampling](https://mlsanity.com/paper/2608.26120/) (2026)
- [METALICA: METAdynamics and repLICA exchange for enhanced diffusion sampling](https://mlsanity.com/paper/2609.17823/) (2026)
- [Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors](https://mlsanity.com/paper/2605.05520/) (2026)
- [Parallel Tempering Initial Sampling in Inference-Time Reward Alignment](https://mlsanity.com/paper/2605.30991/) (2026)
- [Parallel Tempering for Diffusion-Based Combinatorial Optimization](https://mlsanity.com/paper/2609.37323/) (2026)
- [Traversing the Satisfaction-Diversity Frontier in Text-to-Image Diffusion](https://mlsanity.com/paper/2610.02372/) (2026)
- [ENCORE: Exact Non-equilibrium COntrol with Replica Exchange for Diffusion Generation](https://mlsanity.com/paper/2610.02538/) (2026)

## Abstract (arXiv)

Inference-time control of diffusion models aims to steer model outputs to satisfy new constraints without retraining. Previous approaches have mostly relied on heuristic guidance or have been coupled with Sequential Monte Carlo (SMC) for bias correction. In this paper, we propose a flexible alternative based on replica exchange, an algorithm designed initially for sampling problems. We refer to this method as CREPE (Controlling with REPlica Exchange). Unlike SMC, CREPE: (1) generates particles sequentially, (2) maintains high diversity in the generated samples after a burn-in period, and (3) enables online refinement or early termination. We demonstrate its versatility across various tasks, including temperature annealing, reward-tilting, model composition and classifier-free guidance debiasing, with competitive performance compared to prior SMC methods.