Categorical Reparameterization with Denoising Diffusion models

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 \algoname, a novel and efficient diffusion-based soft reparameterization method for categorical distributions. Our approach defines a flexible class of gradient estimators that includes the \sthrough~estimator as a special case. Experiments spanning latent variable models and inference-time reward guidance in discrete diffusion models demonstrate that \algoname\ consistently matches or outperforms existing gradient-based methods.