Iso-Riemannian descent algorithm with convergence analysis under iso-convexity, iso-monotonicity and iso-Lipschitz conditions for optimization on learned Riemannian manifolds from data.
Testing the manifold hypothesis.Journal of the American Mathematical Society, 29(4):983–1049, 2016
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A convex-relaxation denoiser projects PCA-reduced noisy manifold data onto the convex hull using a Gaussian-tail oracle, with finite-sample error bounds under a lower-mass condition on the latent distribution.
λ-Orthogonality regularization enables distribution-specific adaptation of representations via affine transformations while retaining original learned structures.
Aligning the DDIM forward diffusion process with flow-matching manifold evolution enables high-quality generation without time conditioning, and class-conditional synthesis is possible with an unconditional denoiser by using separate time spaces per class.
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Iso-Riemannian Optimization on Learned Data Manifolds
Iso-Riemannian descent algorithm with convergence analysis under iso-convexity, iso-monotonicity and iso-Lipschitz conditions for optimization on learned Riemannian manifolds from data.
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A convex-relaxation denoiser projects PCA-reduced noisy manifold data onto the convex hull using a Gaussian-tail oracle, with finite-sample error bounds under a lower-mass condition on the latent distribution.
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λ-Orthogonality regularization enables distribution-specific adaptation of representations via affine transformations while retaining original learned structures.
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Exploring Time Conditioning in Diffusion Generative Models from Disjoint Noisy Data Manifolds
Aligning the DDIM forward diffusion process with flow-matching manifold evolution enables high-quality generation without time conditioning, and class-conditional synthesis is possible with an unconditional denoiser by using separate time spaces per class.