Avatars Grow Legs: Generating Smooth Human Motion from Sparse Tracking Inputs with Diffusion Model
Yuming Du, Robin Kips, Albert Pumarola, Sebastian Starke, Ali Thabet, Artsiom Sanakoyeu
Optimal Transport and Machine Learning (OTML) Workshop at NeurIPS
Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability in the number of measures, samples and dimensionality. In this work, we propose a multi-marginal optimal transport paradigm based on random one-dimensional projections, whose (generalized) distance we term the sliced multi-marginal Wasserstein distance. To construct this distance, we introduce a characterization of the one-dimensional multi-marginal Kantorovich problem and use it to highlight a number of properties of the sliced multi-marginal Wasserstein distance. In particular, we show that (i) the sliced multi-marginal Wasserstein distance is a (generalized) metric that induces the same topology as the standard Wasserstein distance, (ii) it admits a dimension-free sample complexity, (iii) it is tightly connected with the problem of barycentric averaging under the sliced-Wasserstein metric. We conclude by illustrating the sliced multi-marginal Wasserstein on multi-task density estimation and multi-dynamics reinforcement learning problems.
Yuming Du, Robin Kips, Albert Pumarola, Sebastian Starke, Ali Thabet, Artsiom Sanakoyeu
Bilge Acun, Benjamin Lee, Fiodar Kazhamiaka, Kiwan Maeng, Manoj Chakkaravarthy, Udit Gupta, David Brooks, Carole-Jean Wu
Ilkan Esiyok, Pascal Berrang, Katriel Cohn-Gordon, Robert Künnemann