# Debiasing Guidance for Discrete Diffusion with Sequential Monte Carlo

arXiv: https://arxiv.org/abs/2502.06079 · HTML: https://mlsanity.com/paper/2502.06079/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 32 of its 43 references that are in the map.
- First posted on arXiv 10 Feb 2025.

## Placed in

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

## Builds on (most cited first, 30 of 32)

- [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)
- [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)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation](https://mlsanity.com/paper/1609.08144/) (2016)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [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)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Directly Fine-Tuning Diffusion Models on Differentiable Rewards](https://mlsanity.com/paper/2309.17400/) (2023)
- [DExperts: Decoding-Time Controlled Text Generation with Experts and Anti-Experts](https://mlsanity.com/paper/2105.03023/) (2021)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (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)
- [Likelihood-Based Diffusion Language Models](https://mlsanity.com/paper/2305.18619/) (2023)
- [Denoising Diffusion Samplers](https://mlsanity.com/paper/2302.13834/) (2023)
- [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)
- [Inference-Time Alignment in Diffusion Models with Reward-Guided Generation: Tutorial and Review](https://mlsanity.com/paper/2501.09685/) (2025)
- [Classifier-Free Guidance is a Predictor-Corrector](https://mlsanity.com/paper/2408.09000/) (2024)
- [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)
- [What does guidance do? A fine-grained analysis in a simple setting](https://mlsanity.com/paper/2409.13074/) (2024)
- [Transport meets Variational Inference: Controlled Monte Carlo Diffusions](https://mlsanity.com/paper/2307.01050/) (2023)

## Built on by (most cited first, 30 of 31)

- [Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts](https://mlsanity.com/paper/2503.02819/) (2025)
- [DriftLite: Lightweight Drift Control for Inference-Time Scaling of Diffusion Models](https://mlsanity.com/paper/2509.21655/) (2025)
- [Composition and Control with Distilled Energy Diffusion Models and Sequential Monte Carlo](https://mlsanity.com/paper/2502.12786/) (2025)
- [Split Gibbs Discrete Diffusion Posterior Sampling](https://mlsanity.com/paper/2503.01161/) (2025)
- [Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach](https://mlsanity.com/paper/2506.03979/) (2025)
- [RNE: plug-and-play diffusion inference-time control and energy-based training](https://mlsanity.com/paper/2506.05668/) (2025)
- [Inference-Time Scaling of Discrete Diffusion Models via Importance Weighting and Optimal Proposal Design](https://mlsanity.com/paper/2505.22524/) (2025)
- [Discrete Neural Flow Samplers with Locally Equivariant Transformer](https://mlsanity.com/paper/2505.17741/) (2025)
- [CREPE: Controlling Diffusion with Replica Exchange](https://mlsanity.com/paper/2509.23265/) (2025)
- [Discrete Feynman-Kac Correctors](https://mlsanity.com/paper/2601.10403/) (2026)
- [Steering Generative Models with Experimental Data for Protein Fitness Optimization](https://mlsanity.com/paper/2505.15093/) (2025)
- [Conditional Diffusion Models with Classifier-Free Gibbs-like Guidance](https://mlsanity.com/paper/2505.21101/) (2025)
- [Constrained Diffusion for Protein Design with Hard Structural Constraints](https://mlsanity.com/paper/2510.14989/) (2025)
- [Contrastive Distribution Matching for Amortized Sequential Monte Carlo in Discrete Diffusion](https://mlsanity.com/paper/2605.23346/) (2026)
- [ProSpero: Active Learning for Robust Protein Design Beyond Wild-Type Neighborhoods](https://mlsanity.com/paper/2505.22494/) (2025)
- [PriorGuide: Test-Time Prior Adaptation for Simulation-Based Inference](https://mlsanity.com/paper/2510.13763/) (2025)
- [Foundations of Diffusion Models in General State Spaces: A Self-Contained Introduction](https://mlsanity.com/paper/2512.05092/) (2025)
- [Compression as Adaptation: Implicit Visual Representation with Diffusion Foundation Models](https://mlsanity.com/paper/2603.07615/) (2026)
- [Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential Monte Carlo on Path Measures](https://mlsanity.com/paper/2605.17850/) (2026)
- [Improving Text Style Transfer using Masked Diffusion Language Models with Inference-time Scaling](https://mlsanity.com/paper/2508.10995/) (2025)
- [Deterministic Discrete Denoising](https://mlsanity.com/paper/2509.20896/) (2025)
- [D5P4: Partition Determinantal Point Process for Diversity in Parallel Discrete Diffusion Decoding](https://mlsanity.com/paper/2603.19146/) (2026)
- [BFMT: Enhancing Search Capabilities of Tree Sampler via Bootstrap Flow-Map Tree](https://mlsanity.com/paper/2607.02915/) (2026)
- [FluxLite: Inference-Time Proposal Control for Discrete Diffusion Models](https://mlsanity.com/paper/2609.35947/) (2026)
- [Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Space](https://mlsanity.com/paper/2510.12916/) (2025)
- [Focus on the Core: Empowering Diffusion Large Language Models by Self-Contrast](https://mlsanity.com/paper/2605.01373/) (2026)
- [Sequentially-Controlled Interactive Multi-Particle Flow-Maps for Online Feedback-Driven Search](https://mlsanity.com/paper/2607.01144/) (2026)
- [LATS: Levy Adaptive Tree Sampling for Feedback-Driven Diverse Target Discovery](https://mlsanity.com/paper/2609.06761/) (2026)
- [Parallel Tempering for Diffusion-Based Combinatorial Optimization](https://mlsanity.com/paper/2609.37323/) (2026)
- [Risk-Calibrated Proposal Transport for Finite-Particle Diffusion Steering](https://mlsanity.com/paper/2610.04171/) (2026)

## Abstract (arXiv)

Discrete diffusion models are a class of generative models that produce samples from an approximated data distribution within a discrete state space. Often, there is a need to target specific regions of the data distribution. Current guidance methods aim to sample from a distribution with mass proportional to p0(x0) p(zeta|x0)α but fail to achieve this in practice. We introduce a Sequential Monte Carlo algorithm that generates unbiasedly from this target distribution, utilising the learnt unconditional and guided process. We validate our approach on low-dimensional distributions, controlled images and text generations. For text generation, our method provides strong control while maintaining low perplexity compared to guidance-based approaches.