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Arxiv
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Hessian Geometry of Latent Space in Generative Models
- A novel method for analyzing the latent space geometry of generative models is presented in this paper.
- The method reconstructs the Fisher information metric to analyze statistical physics models and diffusion models.
- It approximates the posterior distribution of latent variables from generated samples to learn the log-partition function.
- The log-partition function defines the Fisher metric for exponential families.
- The method is validated on Ising and TASEP models, outperforming existing baselines in reconstructing thermodynamic quantities.
- When applied to diffusion models, the method reveals a fractal structure of phase transitions in the latent space.
- Phase transitions are characterized by abrupt changes in the Fisher metric.
- Geodesic interpolations are approximately linear within individual phases but break down at phase boundaries.
- At phase boundaries, the diffusion model exhibits a divergent Lipschitz constant with respect to the latent space.
- These findings offer insights into the complex structure of diffusion model latent spaces and their relation to phenomena like phase transitions.
- The method provides theoretical convergence guarantees and source code is available on GitHub.
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