Manifold Diffusion Fields | Ahmed Elhag

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Abstract: We present Manifold Diffusion Fields (MDF), an approach to learn generative models of continuous functions defined over Riemannian manifolds. Leveraging insights from spectral geometry analysis, we define an intrinsic coordinate system on the manifold via the eigen-functions of the Laplace-Beltrami Operator. MDF represents functions using an explicit parametrization formed by a set of multiple input-output pairs. Our approach allows to sample continuous functions on manifolds and is invariant with respect to rigid and isometric transformations of the manifold. Empirical results on several datasets and manifolds show that MDF can capture distributions of such functions with better diversity and fidelity than previous approaches.

Speaker: Ahmed Elhag

Twitter Hannes:   / hannesstaerk  
Twitter Dominique:   / dom_beaini  

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Chapters
00:00 - Intro + Background
07:50 - Manifold Diffusion Fields
12:56 - Method
15:42 - Results
20:25 - From Meshes to Graphs
26:08 - Q+A