ProjFlow: Projection Sampling with Flow Matching for Zero-Shot Exact Spatial Motion Control

TL;DR

ProjFlow is a training-free, zero-shot sampler for human motion generation that enforces exact spatial constraints while maintaining realism, using a novel kinematics-aware metric and a linear inverse problem formulation.

Contribution

It introduces ProjFlow, a novel sampling method that achieves exact constraint satisfaction in human motion generation without training, leveraging a kinematics-aware metric and linear inverse problem approach.

Findings

Achieves exact spatial constraint satisfaction in motion generation.

Maintains or improves motion realism compared to baselines.

Effective in applications like motion inpainting and 2D-to-3D lifting.

Abstract

Generating human motion with precise spatial control is a challenging problem. Existing approaches often require task-specific training or slow optimization, and enforcing hard constraints frequently disrupts motion naturalness. Building on the observation that many animation tasks can be formulated as a linear inverse problem, we introduce ProjFlow, a training-free sampler that achieves zero-shot, exact satisfaction of linear spatial constraints while preserving motion realism. Our key advance is a novel kinematics-aware metric that encodes skeletal topology. This metric allows the sampler to enforce hard constraints by distributing corrections coherently across the entire skeleton, avoiding the unnatural artifacts of naive projection. Furthermore, for sparse inputs, such as filling in long gaps between a few keyframes, we introduce a time-varying formulation using pseudo-observations that fade during sampling. Extensive experiments on representative applications, motion inpainting, and 2D-to-3D lifting, demonstrate that ProjFlow achieves exact constraint satisfaction and matches or improves realism over zero-shot baselines, while remaining competitive with training-based controllers.