Global Convergence of Gradient Descent for Score Matching in Gaussian Mixtures via Reverse Fisher Divergence
arXiv:2606.19876v1 Announce Type: new Abstract: The score matching problem is a central training objective in modern generative modeling, diffusion models, fitting unnormalized statistical models, and inverse problems. A standard approach is to minimize the forward Fisher divergence, where the expectation is taken with respect to the teacher distribution. However, recent results show that even in simple Gaussian mixture model settings, this objective can lead to undesirable and initialization-dependent convergence behavior. In this paper, we study an alternative objective: the reverse Fisher d
The paper addresses a known limitation in current generative modeling techniques (score matching) which is crucial for advancing AI capabilities, particularly in fields like diffusion models.
Improving the convergence behavior of score matching is a fundamental step towards more stable, efficient, and reliable generative AI models, impacting a wide range of AI applications.
The focus shifts from forward Fisher divergence to reverse Fisher divergence, potentially leading to more robust and predictable training outcomes for generative models, moving beyond initialization dependency.
- · AI researchers
- · Generative AI developers
- · Diffusion model applications
- · Companies using unnormalized statistical models
- · Developers stuck with forward Fisher divergence issues
More stable and predictable training of generative AI models like diffusion models.
Accelerated development and deployment of advanced AI applications across various industries due to improved model reliability.
Potentially democratized access to powerful generative AI as training becomes less finicky and more reproducible.
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Read at arXiv cs.LG