# Simple Guidance Mechanisms for Discrete Diffusion Models

arXiv: https://arxiv.org/abs/2412.10193 · HTML: https://mlsanity.com/paper/2412.10193/

## Key facts

- Cited by 155 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 52 of its 68 references that are in the map.
- First posted on arXiv 13 Dec 2024.

## Placed in

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

## Builds on (most cited first, 30 of 52)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Plug and Play Language Models: A Simple Approach to Controlled Text Generation](https://mlsanity.com/paper/1912.02164/) (2019)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [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)
- [CAT3D: Create Anything in 3D with Multi-View Diffusion Models](https://mlsanity.com/paper/2405.10314/) (2024)
- [Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data](https://mlsanity.com/paper/2406.03736/) (2024)
- [FUDGE: Controlled Text Generation With Future Discriminators](https://mlsanity.com/paper/2104.05218/) (2021)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [One Billion Word Benchmark for Measuring Progress in Statistical Language Modeling](https://mlsanity.com/paper/1312.3005/) (2013)

## Built on by (most cited first, 30 of 155)

- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Block Diffusion: Interpolating Between Autoregressive and Diffusion Language Models](https://mlsanity.com/paper/2503.09573/) (2025)
- [Train for the Worst, Plan for the Best: Understanding Token Ordering in Masked Diffusions](https://mlsanity.com/paper/2502.06768/) (2025)
- [Remasking Discrete Diffusion Models with Inference-Time Scaling](https://mlsanity.com/paper/2503.00307/) (2025)
- [The Diffusion Duality](https://mlsanity.com/paper/2506.10892/) (2025)
- [Path Planning for Masked Diffusion Model Sampling](https://mlsanity.com/paper/2502.03540/) (2025)
- [Discrete Diffusion in Large Language and Multimodal Models: A Survey](https://mlsanity.com/paper/2506.13759/) (2025)
- [Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithms](https://mlsanity.com/paper/2502.00234/) (2025)
- [KLASS: KL-Guided Fast Inference in Masked Diffusion Models](https://mlsanity.com/paper/2511.05664/) (2025)
- [Categorical Flow Maps](https://mlsanity.com/paper/2602.12233/) (2026)
- [LangFlow: Continuous Diffusion Rivals Discrete in Language Modeling](https://mlsanity.com/paper/2604.11748/) (2026)
- [Scaling Behavior of Discrete Diffusion Language Models](https://mlsanity.com/paper/2512.10858/) (2025)
- [Esoteric Language Models: A Family of Any-Order Diffusion LLMs](https://mlsanity.com/paper/2506.01928/) (2025)
- [CANDI: Hybrid Discrete-Continuous Diffusion Models](https://mlsanity.com/paper/2510.22510/) (2025)
- [d2: Improving Reasoning in Diffusion Language Models via Trajectory Likelihood Estimation](https://mlsanity.com/paper/2509.21474/) (2025)
- [Scaling Beyond Masked Diffusion Language Models](https://mlsanity.com/paper/2602.15014/) (2026)
- [Target Concrete Score Matching: A Holistic Framework for Discrete Diffusion](https://mlsanity.com/paper/2504.16431/) (2025)
- [Cosmos: Compressed and Smooth Latent Space for Text Diffusion Modeling](https://mlsanity.com/paper/2506.21170/) (2025)
- [Diffuse Everything: Multimodal Diffusion Models on Arbitrary State Spaces](https://mlsanity.com/paper/2506.07903/) (2025)
- [MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Control](https://mlsanity.com/paper/2508.10684/) (2025)
- [Absorb and Converge: Provable Convergence Guarantee for Absorbing Discrete Diffusion Models](https://mlsanity.com/paper/2506.02318/) (2025)
- [Discrete Diffusion Models: Novel Analysis and New Sampler Guarantees](https://mlsanity.com/paper/2509.16756/) (2025)
- [Continuous Diffusion Scales Competitively with Discrete Diffusion for Language](https://mlsanity.com/paper/2605.18530/) (2026)
- [DMax: Aggressive Parallel Decoding for dLLMs](https://mlsanity.com/paper/2604.08302/) (2026)
- [Constrained Discrete Diffusion](https://mlsanity.com/paper/2503.09790/) (2025)
- [CtrlDiff: Boosting Large Diffusion Language Models with Dynamic Block Prediction and Controllable Generation](https://mlsanity.com/paper/2505.14455/) (2025)
- [Taming Masked Diffusion Language Models via Consistency Trajectory Reinforcement Learning with Fewer Decoding Step](https://mlsanity.com/paper/2509.23924/) (2025)
- [Feedback Guidance of Diffusion Models](https://mlsanity.com/paper/2506.06085/) (2025)
- [Ultra-Fast Language Generation via Discrete Diffusion Divergence Instruct](https://mlsanity.com/paper/2509.25035/) (2025)
- [Inference-Time Scaling of Discrete Diffusion Models via Importance Weighting and Optimal Proposal Design](https://mlsanity.com/paper/2505.22524/) (2025)

## Abstract (arXiv)

Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not directly apply to discrete diffusion. Here, we provide a straightforward derivation of classifier-free and classifier-based guidance for discrete diffusion, as well as a new class of diffusion models that leverage uniform noise and that are more guidable because they can continuously edit their outputs. We improve the quality of these models with a novel continuous-time variational lower bound that yields state-of-the-art performance, especially in settings involving guidance or fast generation. Empirically, we demonstrate that our guidance mechanisms combined with uniform noise diffusion improve controllable generation relative to autoregressive and diffusion baselines on several discrete data domains, including genomic sequences, small molecule design, and discretized image generation.