Categorical Reparameterization with Denoising Diffusion Models

Samson Gourevitch, Alain Oliviero Durmus, Eric Moulines, Jimmy Olsson, Yazid Janati
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:36504-36537, 2026.

Abstract

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 ReDGE consistently matches or outperforms existing gradient-based methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-gourevitch26a, title = {Categorical Reparameterization with Denoising Diffusion Models}, author = {Gourevitch, Samson and Oliviero Durmus, Alain and Moulines, Eric and Olsson, Jimmy and Janati, Yazid}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {36504--36537}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/gourevitch26a/gourevitch26a.pdf}, url = {https://proceedings.mlr.press/v306/gourevitch26a.html}, abstract = {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 ReDGE consistently matches or outperforms existing gradient-based methods.} }
Endnote
%0 Conference Paper %T Categorical Reparameterization with Denoising Diffusion Models %A Samson Gourevitch %A Alain Oliviero Durmus %A Eric Moulines %A Jimmy Olsson %A Yazid Janati %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-gourevitch26a %I PMLR %P 36504--36537 %U https://proceedings.mlr.press/v306/gourevitch26a.html %V 306 %X 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 ReDGE consistently matches or outperforms existing gradient-based methods.
APA
Gourevitch, S., Oliviero Durmus, A., Moulines, E., Olsson, J. & Janati, Y.. (2026). Categorical Reparameterization with Denoising Diffusion Models. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:36504-36537 Available from https://proceedings.mlr.press/v306/gourevitch26a.html.

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