# ConFlow: Constraints-Guided Learning with Flow Matching for Motion Generation

arXiv: https://arxiv.org/abs/2607.14424 · HTML: https://mlsanity.com/paper/2607.14424/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 12 of its 15 references that are in the map.
- First posted on arXiv 15 Jul 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 12 of 12)

- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [SE(3)-DiffusionFields: Learning smooth cost functions for joint grasp and motion optimization through diffusion](https://mlsanity.com/paper/2209.03855/) (2022)
- [Gradient Guidance for Diffusion Models: An Optimization Perspective](https://mlsanity.com/paper/2404.14743/) (2024)
- [Multi-Robot Motion Planning with Diffusion Models](https://mlsanity.com/paper/2410.03072/) (2024)
- [Inference-Time Policy Steering through Human Interactions](https://mlsanity.com/paper/2411.16627/) (2024)
- [FlowQ: Energy-Guided Flow Policies for Offline Reinforcement Learning](https://mlsanity.com/paper/2505.14139/) (2025)
- [Language-Guided Object-Centric Diffusion Policy for Generalizable and Collision-Aware Robotic Manipulation](https://mlsanity.com/paper/2407.00451/) (2024)
- [Topology-Matching Normalizing Flows for Out-of-Distribution Detection in Robot Learning](https://mlsanity.com/paper/2311.06481/) (2023)
- [A roadmap for AI in robotics](https://mlsanity.com/paper/2507.19975/) (2025)
- [Constraint-Aware Flow Matching: Decision Aligned End-to-End Training for Constrained Sampling](https://mlsanity.com/paper/2605.12754/) (2026)
- [Guided Decoding for Robot On-line Motion Generation and Adaption](https://mlsanity.com/paper/2403.15239/) (2024)

## Abstract (arXiv)

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 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.