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GenPhys: From Physical Processes to Generative Models (2304.02637v1)

Published 5 Apr 2023 in cs.LG, cs.AI, physics.comp-ph, physics.data-an, and quant-ph

Abstract: Since diffusion models (DM) and the more recent Poisson flow generative models (PFGM) are inspired by physical processes, it is reasonable to ask: Can physical processes offer additional new generative models? We show that the answer is yes. We introduce a general family, Generative Models from Physical Processes (GenPhys), where we translate partial differential equations (PDEs) describing physical processes to generative models. We show that generative models can be constructed from s-generative PDEs (s for smooth). GenPhys subsume the two existing generative models (DM and PFGM) and even give rise to new families of generative models, e.g., "Yukawa Generative Models" inspired from weak interactions. On the other hand, some physical processes by default do not belong to the GenPhys family, e.g., the wave equation and the Schr\"{o}dinger equation, but could be made into the GenPhys family with some modifications. Our goal with GenPhys is to explore and expand the design space of generative models.

Citations (11)

Summary

  • The paper presents the GenPhys framework, which translates physical PDEs into comprehensive generative models.
  • It leverages dispersion relations and s-generative criteria to broaden the theoretical and practical design space of generative models.
  • The framework offers a structured method for innovating efficient, robust AI models inspired by diverse physical processes.

From Physical Processes to Generative Models: A Comprehensive Framework for Generative Modeling

Introduction to GenPhys

Modern advances in generative models have taken inspiration from physical processes, notably highlighted in diffusion models (DMs) and Poisson flow generative models (PFGMs). These models have achieved notable success by tapping into the rich domain of physical phenomena, ranging from thermodynamics to electrostatics. This exploration raises a compelling inquiry: can we systematically extend the principles underlying these models to encompass a broader spectrum of physical processes? The affirmative answer comes in the form of Generative Models from Physical Processes (GenPhys), a framework designed to encapsulate a wide array of physical phenomena into generative models.

GenPhys Framework Overview

The GenPhys framework serves as a bridge connecting physical partial differential equations (PDEs) to generative models. This framework elegantly translates physical PDEs that describe various processes into models capable of data generation. The criteria for PDEs to fit within the GenPhys framework include being s-generative, where the solution to these PDEs should smoothly transition towards a simpler distribution over time. Notably, GenPhys encapsulates a range of models, including those inspired by weak interactions (Yukawa Generative Models), while also positing conditions under which equations like the wave and Schrodinger equations could be adapted to fit within this paradigm.

Expanding the Design Space of Generative Models

One of the significant contributions of GenPhys is the expansion of the design space for generative models. By leveraging the dispersion relations inherent in PDEs, GenPhys offers a principled approach to discerning which physical processes can be transformed into generative models. This endeavor not only broadens the theoretical understanding of the linkage between physics and generative modeling but also opens new avenues for developing models based on a wider variety of physical phenomena.

Practical Implications and Future Directions

The practical implications of GenPhys are multifold. First, it provides a structured methodology for innovating new generative models by drawing from the vast landscape of physical processes. This approach can potentially lead to models that offer advantages in efficiency, robustness, and generation quality over existing models. Secondly, the framework invites further exploration into non-linear PDEs and those without analytical solutions, suggesting that future research could uncover even more versatile and powerful generative models.

Concluding Remarks

In conclusion, Generative Models from Physical Processes (GenPhys) stands as a significant stride towards uniting the realms of physics and generative AI. By delineating a method to convert physical processes described by PDEs into generative models, this framework not only enriches the current landscape of generative models but also sets the stage for future groundbreaking work in this interdisciplinary field. As the exploration of this nexus progresses, the potential for discovery and innovation remains vast, with GenPhys paving the way for a new generation of models inspired by the underlying processes that govern our physical reality.

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