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This paper introduces ConFlow, a novel framework for robot motion generation that integrates task-specific constraints directly into the training objective using differentiable barrier functions. By replacing the standard Gaussian source distribution with a conditional Gaussian Process and employing infeasible demonstrations as negative supervision, ConFlow significantly enhances constraint satisfaction during motion generation. Experiments reveal that ConFlow outperforms traditional flow matching methods in terms of collision rates and trajectory quality, effectively bridging the training-inference gap in generative models.
Training generative motion models with constraints directly integrated into the objective can drastically reduce collision rates and improve trajectory quality in robot navigation tasks.
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.
