# Constrained Code Generation with Discrete Diffusion

arXiv: https://arxiv.org/abs/2605.16829 · HTML: https://mlsanity.com/paper/2605.16829/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 26 of its 31 references that are in the map.
- First posted on arXiv 16 May 2026.

## Placed in

- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)

## Builds on (most cited first, 26 of 26)

- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [SWE-agent: Agent-Computer Interfaces Enable Automated Software Engineering](https://mlsanity.com/paper/2405.15793/) (2024)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Dream 7B: Diffusion Large Language Models](https://mlsanity.com/paper/2508.15487/) (2025)
- [Asleep at the Keyboard? Assessing the Security of GitHub Copilot's Code Contributions](https://mlsanity.com/paper/2108.09293/) (2021)
- [CodeGeeX: A Pre-Trained Model for Code Generation with Multilingual Benchmarking on HumanEval-X](https://mlsanity.com/paper/2303.17568/) (2023)
- [LEVER: Learning to Verify Language-to-Code Generation with Execution](https://mlsanity.com/paper/2302.08468/) (2023)
- [DiffuCoder: Understanding and Improving Masked Diffusion Models for Code Generation](https://mlsanity.com/paper/2506.20639/) (2025)
- [Simple Guidance Mechanisms for Discrete Diffusion Models](https://mlsanity.com/paper/2412.10193/) (2024)
- [Dream-Coder 7B: An Open Diffusion Language Model for Code](https://mlsanity.com/paper/2509.01142/) (2025)
- [LLMSecEval: A Dataset of Natural Language Prompts for Security Evaluations](https://mlsanity.com/paper/2303.09384/) (2023)
- [CWEval: Outcome-driven Evaluation on Functionality and Security of LLM Code Generation](https://mlsanity.com/paper/2501.08200/) (2025)
- [Type-Constrained Code Generation with Language Models](https://mlsanity.com/paper/2504.09246/) (2025)
- [Prompting Techniques for Secure Code Generation: A Systematic Investigation](https://mlsanity.com/paper/2407.07064/) (2024)
- [Constrained Discrete Diffusion](https://mlsanity.com/paper/2503.09790/) (2025)
- [Constrained Decoding of Diffusion LLMs with Context-Free Grammars](https://mlsanity.com/paper/2508.10111/) (2025)
- [From Vulnerabilities to Remediation: A Systematic Literature Review of LLMs in Code Security](https://mlsanity.com/paper/2412.15004/) (2024)
- [Neuro-Symbolic Generative Diffusion Models for Physically Grounded, Robust, and Safe Generation](https://mlsanity.com/paper/2506.01121/) (2025)

## Built on by (most cited first, 1 of 1)

- [Constraints Are Graphs, Not Chains: Exact Decoding for Diffusion Language Models](https://mlsanity.com/paper/2609.32900/) (2026)

## Abstract (arXiv)

Discrete diffusion models are a powerful, emerging paradigm for code generation. They construct programs through iterative refinement of partially corrupted token sequences and enable parallel token refinement. Importantly, this paradigm exposes a global program state at each denoising step, which provides a natural intervention point for enforcing program-level functionality and security constraints, guiding the generation before the final code is committed. Building on this observation, the paper introduces Constrained Diffusion for Code (CDC), a training-free neurosymbolic inference framework that integrates constraint satisfaction directly into the reverse denoising process. CDC augments the base discrete diffusion sampler with constraint-aware denoising operators that combine mathematical optimization with program analysis to identify constraint-relevant regions of the intermediate program state and locally adjust the denoising trajectory, steering generation toward feasible programs while remaining close to the base model. Across code generation benchmarks, CDC consistently improves constraint satisfaction in functional correctness, security, and even syntax, outperforming discrete diffusion and autoregressive baselines with less corrective computation and more localized edits.