Multi-Agent Flow Matching with Decoupled Generative Guidance

Ruoyu Lin; Magnus Egerstedt; Fabio Pasqualetti

cs.LGSep 29, 2026

Multi-Agent Flow Matching with Decoupled Generative Guidance

Authors: Ruoyu Lin, Magnus Egerstedt, Fabio Pasqualetti

Organizations: Department of Electrical Engineering and Computer Science, University of California, Irvine, Irvine, CA 92697 USA · University of North Carolina at Chapel Hill, Chapel Hill, NC 27599 USA

Abstract

Generative modeling is widely used for producing diverse objects from complex, multimodal distributions. However, its expressivity does not, in general, come with formal guarantees that the generated objects satisfy hard constraints or requirements. In multi-agent generation, this problem becomes more challenging because a hard requirement can depend on multiple agents, while each agent may need to determine its own guidance input without relying on the simultaneously computed guidance inputs of other agents. To this end, we introduce DeGG-Flow, a general framework for multi-agent flow matching with decoupled generative guidance. By representing the generative process as a control-affine dynamical system, we develop guidance conditions for two classes of coupled requirements: shared requirements whose satisfaction depends on multiple agents together, and private requirements associated with each individual agent dependent on its neighbors. For both classes, we establish feasibility conditions and finite-horizon convergence guarantees. We further derive a Wasserstein bound that characterizes the distributional deviation induced by the guidance. We demonstrate DeGG-Flow on multi-robot collaboration for crossing a spatial gap by reconfiguring the environment, and on multi-object scene generation with affordance requirements. Across both applications, DeGG-Flow directly generates objects that satisfy all corresponding hard requirements, including at team sizes unseen during training.

Figures & tables

Figure 1: Snapshots of an $N=5$ complete process of Task 1 with SE guidance. Top: the initial configuration. Middle: successful bridge construction. Bottom: spatial gap crossing.

Figure 2: Evolution of $q_{\rm task}$ and its time-varying upper bound $\beta_{\rm task}$ during generative processes for policies generated at early (left), middle (center), and late (right) physical times in the manipulation stage of the example shown in Figure 1 .

$N$	Nominal	Guided
$4$	$46/50$ (92%)	$50/50$ (100%)
$5$	$45/50$ (90%)	$50/50$ (100%)
$6$	$43/50$ (86%)	$50/50$ (100%)
$7$ (unseen)	$42/50$ (84%)	$50/50$ (100%)
$8$ (unseen)	$42/50$ (84%)	$50/50$ (100%)
Overall	$218/250$ (87.2%)	$250/250$ (100%)

Table 1: Success rates for Task 1

$N$	Natural Nominal	Private Nominal	Guided
$4$	$44/50$ (88%)	$36/50$ (72%)	$50/50$ (100%)
$5$	$35/50$ (70%)	$31/50$ (62%)	$50/50$ (100%)
$6$	$32/50$ (64%)	$26/50$ (52%)	$50/50$ (100%)
$7$ (unseen)	$16/50$ (32%)	$13/50$ (26%)	$50/50$ (100%)
$8$ (unseen)	$8/50$ (16%)	$6/50$ (12%)	$50/50$ (100%)
Overall	$135/250$ (54.0%)	$112/250$ (44.8%)	$250/250$ (100%)

Table 2: Success rates for Task 2

Figure 3: An $N=7$ example for Task 2. Green circles represent the objects’ affordance regions that are unobstructed, while the red circle represents one that is obstructed. Left: the scene generated using the nominal vector field satisfies the default right-handed laptop use requirement. Center: the same scene evaluated for a left-handed user, where the required mouse operating region on the left side of the laptop is occupied by a potted plant. Right: PE guidance generates a scene satisfying the left-handed use requirement.

Figure 4: Evolution of $V^{\mathrm{PE}}$ during the generative process for the $N=7$ example in Figure 3 .

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 5: An $N=7$ trial of Task 1. Left: the policies generated by the nominal vector field are driving the plank out of the workspace. Right: the policies with SE guidance lead to successful bridge construction.

Figure 6: Evolution of $q_{\rm safe}$ and its time-varying upper bound $\beta_{\rm safe}$ during a generative process with SE guidance at a physical time right before the policies generated by the nominal vector field drive the plank out of the workspace in an $N=7$ trial.

Figure 7: Training and validation losses over three independent seeds for the GNN-represented nominal vector field in Task 1. Shaded regions represent $\pm$ one sample standard deviation.

Object	Geometry	Affordance region(s)
Drawer organizer	$R(0.156,0.090,0.012)$	$A(\{-0.1,0,0.1\},-0.205,0.108)$
Teacup	$C(0.046)\cup(C(0.019)+(0.061,0))$	$A(0.125,0,0.055)$
Desk lamp	$C(0.06)$	$A(0,-0.147,0.079)$
Laptop	$R(0.085,0.065,0.006)$	$A(0.155,0,0.07)$
Potted plant	$C(0.078)$	$A(0,-0.123,0.062)$
Handled mug	$C(0.067)$	$A(0,-0.141,0.054)$

Appendix

Table 3: Object geometry and default affordance regions for Task 2

Requirement	Natural Nominal	Private Nominal	Guided
Default	$27/50$ (54%)	$27/50$ (54%)	$50/50$ (100%)
Opposite-side access	$27/50$ (54%)	$23/50$ (46%)	$50/50$ (100%)
Side-direction access	$31/50$ (62%)	$23/50$ (46%)	$50/50$ (100%)
Larger affordance region	$23/50$ (46%)	$22/50$ (44%)	$50/50$ (100%)
Combined	$27/50$ (54%)	$17/50$ (34%)	$50/50$ (100%)

Appendix

Table 4: Task 2 results with different affordance requirements.

Figure 8: An $N=8$ example of Task 2. Green circles denote unobstructed affordance regions, a red circle denotes an obstructed affordance region, and red object outlines indicate pairs of objects that are too close to each other. Left: the compact printer and scissors, and the desk lamp and pen cup, are too close to each other, and the drawer organizer obstructs the affordance region of the handled mug. Right: PE guidance resolves all three violations from the same initial sample without any model retraining.

Figure 9: Training and validation flow matching losses over three independent seeds for the nominal vector field in Task 2. Shaded regions represent $\pm$ one sample standard deviation.

Figure 10: Approximation of the Wasserstein distance between the Nominal and Guided distributions in Task 2 with respect the total number of generated objects, normalized by the RMS pairwise distance among the $M=50$ scenes generated by the nominal vector field. The blue and orange curves use the distance metrics in the generative state space and the decoded pose space, respectively.

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Generative models have emerged as a promising paradigm for offline multi-agent reinforcement learning (MARL), but existing approaches require many iterative sampling steps. Recent few-step acceleration methods either distill a joint teacher into independent students or apply averaged velocity fields independently to each agent. Unfortunately, these few-step approaches hurt inter-agent coordination. We show that the efficiency-coordination trade-off is not inherent: single-pass multi-agent generation can preserve coordination when the velocity field is natively joint-coupled. We propose Coordinated few-step Flow (CoFlow), an architecture that combines Coordinated Velocity Attention (CVA) with Adaptive Coordination Gating. A finite-difference consistency surrogate further replaces memory-prohibitive Jacobian-vector product backpropagation through the averaged velocity field with two stop-gradient forward passes. Across 60 configurations spanning MPE, MA-MuJoCo, and SMAC, CoFlow matches or surpasses Gaussian policies, value-based methods, transformer policies, diffusion models, and prior flow baselines on episodic return. Three independent coordination probes confirm that CoFlow's improvements arise from inter-agent coordination rather than per-agent capacity. A denoising-step sweep shows that single-pass inference suffices on every configuration. CoFlow reaches state-of-the-art coordination quality in 1-3 denoising steps under both centralized and decentralized execution. Project Page: https://guowei-zou.github.io/coflow/

Abstract

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