# Diffusion On Syntax Trees For Program Synthesis

arXiv: https://arxiv.org/abs/2405.20519 · HTML: https://mlsanity.com/paper/2405.20519/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 22 of its 42 references that are in the map.
- First posted on arXiv 30 May 2024.

## Placed in

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

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Improved Baselines with Visual Instruction Tuning](https://mlsanity.com/paper/2310.03744/) (2023)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Multimodal Few-Shot Learning with Frozen Language Models](https://mlsanity.com/paper/2106.13884/) (2021)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [High-Performance Large-Scale Image Recognition Without Normalization](https://mlsanity.com/paper/2102.06171/) (2021)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [GFlowNet Foundations](https://mlsanity.com/paper/2111.09266/) (2021)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [DeepCoder: Learning to Write Programs](https://mlsanity.com/paper/1611.01989/) (2016)
- [RobustFill: Neural Program Learning under Noisy I/O](https://mlsanity.com/paper/1703.07469/) (2017)
- [InferFix: End-to-End Program Repair with LLMs](https://mlsanity.com/paper/2303.07263/) (2023)
- [CSGNet: Neural Shape Parser for Constructive Solid Geometry](https://mlsanity.com/paper/1712.08290/) (2017)
- [Write, Execute, Assess: Program Synthesis with a REPL](https://mlsanity.com/paper/1906.04604/) (2019)
- [Learning to Infer Graphics Programs from Hand-Drawn Images](https://mlsanity.com/paper/1707.09627/) (2017)
- [CoditT5: Pretraining for Source Code and Natural Language Editing](https://mlsanity.com/paper/2208.05446/) (2022)
- [CODIT: Code Editing with Tree-Based Neural Models](https://mlsanity.com/paper/1810.00314/) (2018)
- [Superion: Grammar-Aware Greybox Fuzzing](https://mlsanity.com/paper/1812.01197/) (2018)
- [On the Training Instability of Shuffling SGD with Batch Normalization](https://mlsanity.com/paper/2302.12444/) (2023)

## Built on by (most cited first, 10 of 10)

- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [TikZero: Zero-Shot Text-Guided Graphics Program Synthesis](https://mlsanity.com/paper/2503.11509/) (2025)
- [Towards Efficient Neurally-Guided Program Induction for ARC-AGI](https://mlsanity.com/paper/2411.17708/) (2024)
- [DiffCSG: Differentiable CSG via Rasterization](https://mlsanity.com/paper/2409.01421/) (2024)
- [MultiMat: Multimodal Program Synthesis for Procedural Materials using Large Multimodal Models](https://mlsanity.com/paper/2509.22151/) (2025)
- [Estimating Probability Densities with Transformer and Denoising Diffusion](https://mlsanity.com/paper/2407.15703/) (2024)
- [See it. Say it. Sorted: Agentic System for Compositional Diagram Generation](https://mlsanity.com/paper/2508.15222/) (2025)
- [Bridging Vision, Language, and Mathematics: Pictographic Character Reconstruction with B'ezier Curves](https://mlsanity.com/paper/2511.00076/) (2025)
- [LLMs + Security = Trouble](https://mlsanity.com/paper/2602.08422/) (2026)
- [Beyond the Autoregressive Horizon: A Comprehensive Survey of Diffusion Models, World Modelling, and State Space Models for Code](https://mlsanity.com/paper/2606.23690/) (2026)

## Abstract (arXiv)

Large language models generate code one token at a time. Their autoregressive generation process lacks the feedback of observing the program's output. Training LLMs to suggest edits directly can be challenging due to the scarcity of rich edit data. To address these problems, we propose neural diffusion models that operate on syntax trees of any context-free grammar. Similar to image diffusion models, our method also inverts ``noise'' applied to syntax trees. Rather than generating code sequentially, we iteratively edit it while preserving syntactic validity, which makes it easy to combine this neural model with search. We apply our approach to inverse graphics tasks, where our model learns to convert images into programs that produce those images. Combined with search, our model is able to write graphics programs, see the execution result, and debug them to meet the required specifications. We additionally show how our system can write graphics programs for hand-drawn sketches.