# SketchDNN: Joint Continuous-Discrete Diffusion for CAD Sketch Generation

arXiv: https://arxiv.org/abs/2507.11579 · HTML: https://mlsanity.com/paper/2507.11579/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Image generation, text-to-image and editing, one of 14 directions in Diffusion models.
- Builds on 28 of its 35 references that are in the map.
- First posted on arXiv 15 Jul 2025.

## Placed in

- Diffusion models / [Image generation, text-to-image and editing](https://mlsanity.com/diffusion/image-generation-text-to-image-and-editing/)

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [DeepCAD: A Deep Generative Network for Computer-Aided Design Models](https://mlsanity.com/paper/2105.09492/) (2021)
- [Autoregressive Diffusion Models](https://mlsanity.com/paper/2110.02037/) (2021)
- [SSD-LM: Semi-autoregressive Simplex-based Diffusion Language Model for Text Generation and Modular Control](https://mlsanity.com/paper/2210.17432/) (2022)
- [SkexGen: Autoregressive Generation of CAD Construction Sequences with Disentangled Codebooks](https://mlsanity.com/paper/2207.04632/) (2022)
- [BrepGen: A B-rep Generative Diffusion Model with Structured Latent Geometry](https://mlsanity.com/paper/2401.15563/) (2024)
- [Computer-Aided Design as Language](https://mlsanity.com/paper/2105.02769/) (2021)
- [A Review of the Gumbel-max Trick and its Extensions for Discrete Stochasticity in Machine Learning](https://mlsanity.com/paper/2110.01515/) (2021)
- [HouseDiffusion: Vector Floorplan Generation via a Diffusion Model with Discrete and Continuous Denoising](https://mlsanity.com/paper/2211.13287/) (2022)
- [Unleashing Transformers: Parallel Token Prediction with Discrete Absorbing Diffusion for Fast High-Resolution Image Generation from Vector-Quantized Codes](https://mlsanity.com/paper/2111.12701/) (2021)
- [Latent Diffusion Energy-Based Model for Interpretable Text Modeling](https://mlsanity.com/paper/2206.05895/) (2022)
- [Vitruvion: A Generative Model of Parametric CAD Sketches](https://mlsanity.com/paper/2109.14124/) (2021)
- [TESS: Text-to-Text Self-Conditioned Simplex Diffusion](https://mlsanity.com/paper/2305.08379/) (2023)
- [Engineering Sketch Generation for Computer-Aided Design](https://mlsanity.com/paper/2104.09621/) (2021)
- [PLay: Parametrically Conditioned Layout Generation using Latent Diffusion](https://mlsanity.com/paper/2301.11529/) (2023)
- [DLT: Conditioned layout generation with Joint Discrete-Continuous Diffusion Layout Transformer](https://mlsanity.com/paper/2303.03755/) (2023)
- [Permutation Equivariance of Transformers and Its Applications](https://mlsanity.com/paper/2304.07735/) (2023)
- [Invertible Gaussian Reparameterization: Revisiting the Gumbel-Softmax](https://mlsanity.com/paper/1912.09588/) (2019)
- [Diffusion bridges vector quantized Variational AutoEncoders](https://mlsanity.com/paper/2202.04895/) (2022)

## Built on by (most cited first, 5 of 5)

- [ReCAD: Reinforcement Learning Enhanced Parametric CAD Model Generation with Vision-Language Models](https://mlsanity.com/paper/2512.06328/) (2025)
- [JointDiff: Bridging Continuous and Discrete in Multi-Agent Trajectory Generation](https://mlsanity.com/paper/2509.22522/) (2025)
- [Simplex-to-Euclidean Bijections for Categorical Flow Matching](https://mlsanity.com/paper/2510.27480/) (2025)
- [CADENA: Stepwise CAD Reverse Engineering](https://mlsanity.com/paper/2608.00799/) (2026)
- [Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process Classification](https://mlsanity.com/paper/2603.16621/) (2026)

## Abstract (arXiv)

We present SketchDNN, a generative model for synthesizing CAD sketches that jointly models both continuous parameters and discrete class labels through a unified continuous-discrete diffusion process. Our core innovation is Gaussian-Softmax diffusion, where logits perturbed with Gaussian noise are projected onto the probability simplex via a softmax transformation, facilitating blended class labels for discrete variables. This formulation addresses 2 key challenges, namely, the heterogeneity of primitive parameterizations and the permutation invariance of primitives in CAD sketches. Our approach significantly improves generation quality, reducing Fr'echet Inception Distance (FID) from 16.04 to 7.80 and negative log-likelihood (NLL) from 84.8 to 81.33, establishing a new state-of-the-art in CAD sketch generation on the SketchGraphs dataset.