Zero-Variance Gradients for Variational Autoencoders

• URL: http://arxiv.org/abs/2508.03587v1
• Date: Tue, 05 Aug 2025 15:54:21 GMT
• Title: Zero-Variance Gradients for Variational Autoencoders
• Authors: Zilei Shao, Anji Liu, Guy Van den Broeck,
• Abstract summary: Training deep generative models like Variational Autoencoders (VAEs) is often hindered by the need to backpropagate gradients through sampling of their latent variables.<n>In this paper, we propose a new perspective that sidesteps this problem, which we call Silent Gradients.<n>Instead of improving estimators, we leverage specific decoder architectures analytically to compute the expected ELBO, yielding a gradient with zero variance.
• Score: 32.818968022327866
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Training deep generative models like Variational Autoencoders (VAEs) is often hindered by the need to backpropagate gradients through the stochastic sampling of their latent variables, a process that inherently introduces estimation variance, which can slow convergence and degrade performance. In this paper, we propose a new perspective that sidesteps this problem, which we call Silent Gradients. Instead of improving stochastic estimators, we leverage specific decoder architectures to analytically compute the expected ELBO, yielding a gradient with zero variance. We first provide a theoretical foundation for this method and demonstrate its superiority over existing estimators in a controlled setting with a linear decoder. To generalize our approach for practical use with complex, expressive decoders, we introduce a novel training dynamic that uses the exact, zero-variance gradient to guide the early stages of encoder training before annealing to a standard stochastic estimator. Our experiments show that this technique consistently improves the performance of established baselines, including reparameterization, Gumbel-Softmax, and REINFORCE, across multiple datasets. This work opens a new direction for training generative models by combining the stability of analytical computation with the expressiveness of deep, nonlinear architecture.

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