Sparse Compositional Flow Matching by geometric assembly from motion primitives
Authors: Yan Tang, Yuanbo Tang, Tingyu Cao, Shaolun Huang, Yang Li
Organizations: Tsinghua Shenzhen Graduate School, Tsinghua University, Shenzhen, China · School of AI, Chinese University of Hong Kong (Shenzhen)
Abstract
Embodied trajectories, such as the executable motion sequences of robotic manipulators, underwater vehicles, and mobile robots, are a fundamental output of embodied AI. Modern generative models often treat them as a dense, monolithic signal generated point by point, fitting an intricate high-dimensional posterior while leaving the data's latent structure unmodeled, the same sample inefficiency long identified by the structured generative model literature. We argue that a compositional latent structure is a natural choice: many embodied tasks share recurring motion fragments that can be made explicit as a finite repertoire of reusable motion primitives, and compositional units naturally align with subtask boundaries to support task decomposition. Existing compositional generators, however, compose in a latent space and rely on post-hoc decoding to relate sampled units to actual trajectory segments. We instead compose directly in the physical trajectory space through a flow-matching framework with two coupled designs. Motion-Primitive Dictionary Learning equips each atom with a learnable length mask and binary starting indicators so the atom itself is the primitive, reused verbatim wherever it is placed. Structural Sparse Flow Matching with Geometric Constraints then generates a binary placement matrix using duration-aware tokenization and a differentiable geometric loss that enforces spatial continuity and temporal contiguity where adjacent primitives meet. On Open X-Embodiment and 3DMoTraj, the framework attains state-of-the-art accuracy and reduces the FDE/ADE ratio from 1.8 to 1.07, improving ADE by 19.2% and FDE by 21.0% over the strongest baseline.
In recent years Flow Matching has become a prominent method for generative modeling robot motion generation. In its generic form Flow Matching is an ODE-based neural sampler that is trained by regressing empirical flow fields associated with motion samples as data. However, in robot motion generation we often have additional constraints that might not be present in the collected data. The majority of current approaches train the flow on the available data and use inference-time guidance to enforce task-specific constraints. To address this mismatch, we propose \textbf{ConFlow}, a constraint-guided flow matching framework that incorporates constraint information directly into the training objective via differentiable barrier or cost functions. To address design specifications such as smoothness and boundary conditions, we propose replacing the standard Gaussian source distribution used in flow matching training with a conditional Gaussian Process. Our approach also uses infeasible demonstrations as negative supervision, improving constraint satisfaction without requiring additional expert data. Experiments on a two-robot navigation task demonstrate that ConFlow achieves lower collision rates and higher trajectory quality than standard flow matching baselines, with or without inference-time guidance. These results validate training-time constraint integration as an effective approach to closing the training--inference gap in generative motion models.
Text-to-motion generation must produce motions that are semantically correct, temporally coherent, and physically plausible. A natural approach is to first project motion data into a structured semantic space and then train a generative model within that space. Such a paradigm has been highly successful in image generation through Representation Autoencoders (RAEs), where a frozen self-supervised encoder provides semantic features for diffusion or flow models to learn from. However, direct transfer of such a paradigm to motion space using Motion-JEPA as the frozen encoder fails dramatically. We diagnose this failure geometrically and identify two motion-specific bottlenecks: (1) the JEPA feature space is spectrally ill-conditioned, making the Gaussian-to-data transport unstable; and (2) even with a well-conditioned spectrum, flow residuals tend to align with decoder-sensitive directions, where small latent errors are amplified into large motion artifacts after decoding. Based on these insights, we propose MoRAE. MoRAE addresses the two bottlenecks separately. A compact bottleneck distills the structured JEPA representation while removing weak and redundant directions, bringing the latent spectrum into a transport-stable regime. Motion-coupled training then aligns the retained latent geometry with the decoder, making characteristic flow errors less costly after decoding. With this flow-friendly latent, a standard non-autoregressive Flow-Matching DiT achieves state-of-the-art performance.
Text-to-motion generation requires modeling both global action structure and fine-grained motion dynamics from natural language. Existing approaches typically rely on either continuous diffusion models or vector-quantized discrete representations. Diffusion models generate smooth motions but lack explicit compositional structure for temporal planning, while discrete token-based methods improve controllability but compress motion into finite codebooks, losing fine-grained dynamics. We argue that this limitation stems from a representation mismatch: action semantics such as intent, phase transitions, and temporal layout are inherently discrete and compositional, whereas joint trajectories and motion dynamics are continuous and locally correlated. To address this, we propose DC-Motion, a discrete-continuous factorized framework for human motion generation. DC-Motion decomposes motion into discrete structural tokens capturing global action layout and continuous residual latents modeling fine-grained dynamics. A text-conditioned structure generator predicts discrete tokens via iterative masked modeling, and a diffusion-based residual generator produces continuous motion conditioned on the structure. Experiments on HumanML3D and KIT-ML demonstrate that DC-Motion achieves strong performance in both FID and R-Precision, outperforming representative diffusion-based and discrete-token baselines.