Université Paris Sciences et Lettres

Discrete diffusion models have lacked the statistical theory that continuous diffusion enjoys, and it was unclear whether they can exploit sparse structure in the data distribution. This analysis casts masked-diffusion score estimation as a per-context label-smoothed classifier and shows the smoothing is equivalent to regularizing with the score loss of the uniform distribution. On sparse distributions where at most k sequences have positive probability, the terminal laws of both masked and uniform noising attain the sparse minimax rate, and the smoothing level can be chosen adaptively from the number of distinct training sequences without knowing the sparsity parameter.

Discrete diffusion models have lacked the statistical theory that continuous diffusion enjoys, and it was unclear whether they can exploit sparse structure in the data distribution. This analysis casts masked-diffusion score estimation as a per-context label-smoothed classifier and shows the smoothing is equivalent to regularizing with the score loss of the uniform distribution. On sparse distributions where at most k sequences have positive probability, the terminal laws of both masked and uniform noising attain the sparse minimax rate, and the smoothing level can be chosen adaptively from the number of distinct training sequences without knowing the sparsity parameter.

OTRetarget jointly retargets robot and multi-object motion by representing surface interactions through signed distances, closest surface points and relative directions, transferring these quantities across human, robot and object geometries with entropic optimal transport, and enforcing them in a per-frame constrained inverse kinematics that optimizes robot and object poses jointly; on OMOMO it reaches a robot-object interaction Jaccard of 87% and a depth error of 8.7 mm versus 28% and 29.3 mm for OmniRetarget, and transfers to a physical Unitree G1 for two-handed box pick-and-place onto a table.

OTRetarget jointly retargets robot and multi-object motion by representing surface interactions through signed distances, closest surface points and relative directions, transferring these quantities across human, robot and object geometries with entropic optimal transport, and enforcing them in a per-frame constrained inverse kinematics that optimizes robot and object poses jointly; on OMOMO it reaches a robot-object interaction Jaccard of 87% and a depth error of 8.7 mm versus 28% and 29.3 mm for OmniRetarget, and transfers to a physical Unitree G1 for two-handed box pick-and-place onto a table.