Understanding Diffusion Models Using Feynman's Path Integral

Kernekoncepter

Utilizing the path integral framework to deepen understanding of diffusion models and evaluate noise impact.

Resumé

The article explores diffusion models using Feynman's path integral formulation. It delves into the performance disparity between stochastic and deterministic sampling schemes. The formulation connects quantum physics concepts to generative models, enabling a comprehensive description. By introducing an interpolating parameter, the article identifies its role akin to Planck's constant in quantum physics. The Wentzel–Kramers–Brillouin expansion is applied to assess performance disparities between sampling schemes. The article also discusses reverse-time SDEs, loss functions, and likelihood calculations in diffusion models.

Statistik

Score-based diffusion models have proven effective in image generation.
Stochastic sampling processes require more function evaluations than deterministic ones.
Noise within stochastic generation can enhance diversity and quality of generated samples.
The path integral formalism generalizes trajectories including quantum fluctuations.
The path integral formulation enables various techniques from quantum physics to be applied.

Citater

"The analogy between h and ℏ naturally leads us to explore a perturbative expansion in terms of h."
"This analogy provides a physical interpretation of the limit as h → 0; it realizes the classical limit in the path integral representation."
"The deviation caused by h ̸= 0 is quantified by δxt, representing how noise influences the bijective relationship between data points."

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Understanding Diffusion Models by Feynman's Path Integral

by Yuji Hirono,... kl. arxiv.org 03-19-2024

https://arxiv.org/pdf/2403.11262.pdf

Dybere Forespørgsler

How does the application of the WKB expansion enhance our understanding of noise impact in generative models

The application of the WKB expansion in generative models, specifically in understanding noise impact, provides a deeper insight into how different levels of noise affect the quality of generated samples. By perturbatively evaluating the negative log-likelihood with respect to a parameter like Planck's constant in quantum physics (analogous to noise level), we can quantify the impact of noise on sample generation. The WKB expansion allows us to analyze how small deviations from perfect score estimation influence the overall performance of generative models. This method helps us understand how introducing noise can either enhance diversity and quality or potentially degrade it based on specific model configurations.

What are potential implications for applying path integral formalism to other areas beyond diffusion models

Applying path integral formalism beyond diffusion models opens up various possibilities for exploring other areas where complex probabilistic modeling is involved. One potential implication is in understanding Bayesian inference and probabilistic graphical models more deeply by leveraging the path integral framework. This approach could provide new insights into sampling techniques, loss functions, and optimization strategies used in these domains. Additionally, applying path integrals to reinforcement learning algorithms may offer novel perspectives on policy optimization and value function approximation methods.

How might imperfect score estimation affect the overall quality of generated images

Imperfect score estimation can significantly impact the overall quality of generated images in generative models. When there are inaccuracies in estimating scores that guide sample generation, it can lead to distorted or less realistic outputs. These imperfections may result in mode collapse, where certain modes dominate while others are neglected during sampling processes. As a consequence, the diversity and fidelity of generated images may be compromised due to inaccurate guidance provided by imperfect score estimations. Therefore, ensuring accurate scoring mechanisms is crucial for maintaining high-quality output images in generative models.