# Categorical Reparameterization with Denoising Diffusion models

arXiv: https://arxiv.org/abs/2601.00781 · HTML: https://mlsanity.com/paper/2601.00781/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 45 of its 57 references that are in the map.
- First posted on arXiv 2 Jan 2026.

## Placed in

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

## Builds on (most cited first, 30 of 45)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Dota 2 with Large Scale Deep Reinforcement Learning](https://mlsanity.com/paper/1912.06680/) (2019)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speech](https://mlsanity.com/paper/2105.06337/) (2021)
- [Continuous diffusion for categorical data](https://mlsanity.com/paper/2211.15089/) (2022)
- [Image Restoration with Mean-Reverting Stochastic Differential Equations](https://mlsanity.com/paper/2301.11699/) (2023)
- [Beyond Autoregression: Discrete Diffusion for Complex Reasoning and Planning](https://mlsanity.com/paper/2410.14157/) (2024)
- [Gradient Estimation Using Stochastic Computation Graphs](https://mlsanity.com/paper/1506.05254/) (2015)
- [Neural Variational Inference and Learning in Belief Networks](https://mlsanity.com/paper/1402.0030/) (2014)
- [Backpropagation through the Void: Optimizing control variates for black-box gradient estimation](https://mlsanity.com/paper/1711.00123/) (2017)

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

- [IDRF: Inverse-Distilled Reward Fine-tuning of Masked Discrete Diffusion Models](https://mlsanity.com/paper/2610.03641/) (2026)

## Abstract (arXiv)

Learning models with categorical variables requires optimizing expectations over discrete distributions, a setting in which stochastic gradient-based optimization is challenging due to the non-differentiability of categorical sampling. A common workaround is to replace the discrete distribution with a continuous relaxation, yielding a smooth surrogate that admits reparameterized gradient estimates via the reparameterization trick. Building on this idea, we introduce ReDGE, a novel and efficient diffusion-based soft reparameterization method for categorical distributions. Our approach defines a flexible class of gradient estimators that includes the Straight-Through estimator as a special case. Experiments spanning latent variable models and inference-time reward guidance in discrete diffusion models demonstrate that ReDGE consistently matches or outperforms existing gradient-based methods. The code will be made available at https://github.com/samsongourevitch/redge.