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About this paper
Luis A. Pérez Rey, Vlado Menkovski, Jacobus W. Portegies
Diffusion Variational Autoencoders (∆VAEs) introduce a framework allowing arbitrary Riemannian submanifolds as VAE latent spaces, addressing the 'manifold mismatch' problem. The method employs an approximate reparameterization trick and an asymptotic KL-divergence approximation, demonstrating effective topological capture for synthetic data and broad applicability to datasets like MNIST with comparable performance.
Key insights
- Aligning the VAE's latent space topology with the intrinsic topology of the data can lead to more accurate and interpretable representations of underlying generative factors, overcoming limitations of Euclidean latent spaces.
- A random walk-based approximation for the reparameterization trick offers a practical approach to enable gradient-based optimization for VAEs with general non-Euclidean latent spaces.
- Asymptotic approximations of the KL divergence based on the heat kernel facilitate efficient training of manifold VAEs by addressing the intractability of exact computation for general Riemannian manifolds.
Summary by alphaXiv.
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