Inverse Engineering Diffusion: Deriving Variance Schedules with Rationale
Keywords: diffusion models, generative models, score-based generative models, generative modeling, stochastic differential equations
TL;DR: We introduce a novel perspective on score-based diffusion models, viewing the inverse of the variance schedule as a CDF and its derivative as a PDF, which enables us to define a variance schedule from its density (i.e., probabilistic rationale).
Abstract: A fundamental aspect of diffusion models is the variance schedule, which governs the evolution of variance throughout the diffusion process. Despite numerous studies exploring variance schedules, little effort has been made to understand the variance distributions implied by sampling from these schedules and how it benefits both training and data generation. We introduce a novel perspective on score-based diffusion models, bridging the gap between the variance schedule and its underlying variance distribution. Specifically, we propose the notion of sampling variance according to a probabilistic rationale, which induces a density. Our approach views the inverse of the variance schedule as a cumulative distribution function (CDF) and its first derivative as a probability density function (PDF) of the variance distribution. This formulation not only offers a unified view of variance schedules but also allows for the direct engineering of a variance schedule from the probabilistic rationale of its inverse function. Additionally, our framework is not limited to CDFs with closed-form inverse solutions, enabling the exploration of variance schedules that are unattainable through conventional methods. We present the tools required to obtain a diverse array of novel variance schedules tailored to specific rationales, such as separability metrics or prior beliefs. These schedules may exhibit varied dynamics, ranging from rapid convergence towards zero to prolonged periods in high-variance regions. Through comprehensive empirical evaluation, we demonstrate the efficacy of enhancing the performance of diffusion models with schedules distinct from those encountered during training. We provide a principled and unified approach to variance schedules in diffusion models, revealing the relationship between variance schedules and their underlying probabilistic rationales, which yields notable improvements in image generation performance, as measured by FID.
Primary Area: generative models
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Submission Number: 4931
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