# Reward-Guided Discrete Diffusion via Clean-Sample Markov Chain for Molecule and Biological Sequence Design

arXiv: https://arxiv.org/abs/2602.09424 · HTML: https://mlsanity.com/paper/2602.09424/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 36 of its 53 references that are in the map.
- First posted on arXiv 10 Feb 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 36)

- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [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)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [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)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [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)
- [Score-based Continuous-time Discrete Diffusion Models](https://mlsanity.com/paper/2211.16750/) (2022)
- [Simple Guidance Mechanisms for Discrete Diffusion Models](https://mlsanity.com/paper/2412.10193/) (2024)
- [Concrete Score Matching: Generalized Score Matching for Discrete Data](https://mlsanity.com/paper/2211.00802/) (2022)
- [Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decoding](https://mlsanity.com/paper/2408.08252/) (2024)
- [Unlocking Guidance for Discrete State-Space Diffusion and Flow Models](https://mlsanity.com/paper/2406.01572/) (2024)
- [Dirichlet Flow Matching with Applications to DNA Sequence Design](https://mlsanity.com/paper/2402.05841/) (2024)
- [Test-time Alignment of Diffusion Models without Reward Over-optimization](https://mlsanity.com/paper/2501.05803/) (2025)
- [Inference-Time Alignment in Diffusion Models with Reward-Guided Generation: Tutorial and Review](https://mlsanity.com/paper/2501.09685/) (2025)
- [Path Planning for Masked Diffusion Model Sampling](https://mlsanity.com/paper/2502.03540/) (2025)
- [Fine-Tuning Discrete Diffusion Models via Reward Optimization with Applications to DNA and Protein Design](https://mlsanity.com/paper/2410.13643/) (2024)
- [Elements of Sequential Monte Carlo](https://mlsanity.com/paper/1903.04797/) (2019)
- [Think While You Generate: Discrete Diffusion with Planned Denoising](https://mlsanity.com/paper/2410.06264/) (2024)
- [Learning Diffusion Priors from Observations by Expectation Maximization](https://mlsanity.com/paper/2405.13712/) (2024)
- [Informed Correctors for Discrete Diffusion Models](https://mlsanity.com/paper/2407.21243/) (2024)
- [GenMol: A Drug Discovery Generalist with Discrete Diffusion](https://mlsanity.com/paper/2501.06158/) (2025)

## Built on by (most cited first, 6 of 6)

- [Contrastive Distribution Matching for Amortized Sequential Monte Carlo in Discrete Diffusion](https://mlsanity.com/paper/2605.23346/) (2026)
- [VGAS: Variance-Reduced Guidance and Adaptive Selection for Training-Free Reward Alignment in Discrete Diffusion](https://mlsanity.com/paper/2608.26585/) (2026)
- [Grab a Coffee: Future-Aware Guidance for Discrete Diffusion with Compiled Objectives](https://mlsanity.com/paper/2609.35924/) (2026)
- [D-DOIT: Training-free Adaptation of Discrete Diffusion via Doob's h-Transform](https://mlsanity.com/paper/2610.04938/) (2026)
- [Noise, Denoise, Correct: MCMC Posterior Sampling with Diffusion Priors in Three Steps](https://mlsanity.com/paper/2610.09407/) (2026)
- [Learning Graph Energies for Finite-Time Generation](https://mlsanity.com/paper/2610.19946/) (2026)

## Abstract (arXiv)

Discrete diffusion models have recently emerged as a powerful class of generative models for chemistry and biology data. In these fields, the goal is to generate various samples with high rewards (e.g., drug-likeness in molecules), making reward-based guidance crucial. Most existing methods are based on guiding the diffusion model using intermediate rewards but tend to underperform since intermediate rewards are noisy due to the non-smooth nature of reward functions used in scientific domains. To address this, we propose Clean-Sample Markov Chain (CSMC) Sampler, a method that performs effective test-time reward-guided sampling for discrete diffusion models, enabling local search without relying on intermediate rewards. CSMC constructs a Markov chain of clean samples using the Metropolis-Hastings algorithm such that its stationary distribution is the target distribution. We design a proposal distribution by sequentially applying the forward and backward diffusion processes, making the acceptance probability tractable. Experiments on molecule and biological sequence generation with various reward functions demonstrate that our method consistently outperforms prior approaches that rely on intermediate rewards.