Riemannian archetypal analysis projects data onto a manifold of geodesically convex archetype combinations via pullback geometry on deformed star distributions.
Chen et al
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abstract
Generative modeling aims to generate new data samples that resemble a given dataset. When using diffusion models for this task, one of the main challenges is solving the problem in the input space, which tends to be very high-dimensional. To address this, recent approaches solve diffusion models in the latent space through an encoder that maps from the data space to a lower-dimensional latent space, improving training efficiency and achieving state-of-the-art results. The variational autoencoder (VAE) is the most commonly used encoder/decoder framework in this domain, known for its ability to learn latent representations and generate data samples. In this paper, we introduce a novel encoder/decoder framework with theoretical properties distinct from those of the VAE, specifically designed to preserve the geometric structure of the data distribution. We demonstrate the significant advantages of this geometry-preserving encoder in the training process of both the encoder and decoder. Additionally, we provide theoretical results proving convergence of the training process, including convergence guarantees for encoder training, and results showing faster convergence of decoder training when using the geometry-preserving encoder.
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Imagine2Real enables zero-shot humanoid-object interaction by unifying motions as 4D point trajectories, tracking only base/hands/object keypoints inside a BFM latent space, and training with progressive simple rewards for mocap deployment.
Latent diffusability is quantified by decomposing the MMSE rate along diffusion trajectories into Fisher Information and Fisher Information Rate, with three geometric penalties (dimensional compression, tangential distortion, curvature injection) identified as sources of failure.
citing papers explorer
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Riemannian Archetypal Analysis: Interpretable non-linear data analysis on deformed star distributions
Riemannian archetypal analysis projects data onto a manifold of geodesically convex archetype combinations via pullback geometry on deformed star distributions.
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Imagine2Real: Towards Zero-shot Humanoid-Object Interaction via Video Generative Priors
Imagine2Real enables zero-shot humanoid-object interaction by unifying motions as 4D point trajectories, tracking only base/hands/object keypoints inside a BFM latent space, and training with progressive simple rewards for mocap deployment.
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Understanding Latent Diffusability via Fisher Geometry
Latent diffusability is quantified by decomposing the MMSE rate along diffusion trajectories into Fisher Information and Fisher Information Rate, with three geometric penalties (dimensional compression, tangential distortion, curvature injection) identified as sources of failure.