AegisFlow: Training-Free Non-Myopic Path-Safe Guided Flow Matching

Kunpeng Liu; Boshi Zhang; Keyou You

cs.AIOct 29, 2026

AegisFlow: Training-Free Non-Myopic Path-Safe Guided Flow Matching

Authors: Kunpeng Liu, Boshi Zhang, Keyou You

Organizations: Department of Automation and BNRist, Tsinghua University, Beijing, China

Abstract

Pretrained generative models, such as diffusion and flow matching models, have demonstrated exceptional capabilities in synthesizing high-quality data. However, steering their generative trajectories to satisfy strict constraints--such as identity preservation in image editing or obstacle avoidance in robotics--remains fundamentally challenging. While recent training-free guidance methods enforce path-safety, they rely heavily on min-norm controllers that only account for immediate constraint satisfaction. These myopic approaches often yield suboptimal trajectories that hover dangerously close to the boundary, severely restricting the model's ability to optimize toward its target. In this paper, we propose AegisFlow, a training-free, non-myopic path-safe guidance framework that recasts guided generation as a safety-critical optimal control problem with global scope. By integrating a time-varying barrier function directly into the global cost functional, AegisFlow naturally enforces constraints along the entire generative path. To compute the global optimal control, we derive a tractable, mathematically grounded approximation of the Hamilton-Jacobi-Bellman (HJB) equation. Comprehensive experiments demonstrate that AegisFlow outperforms state-of-the-art methods across text-guided image manipulation and robotic planning, establishing a significantly better trade-off between target alignment and constraint satisfaction. Code is available at https://github.com/LiuKunpeng03/AegisFlow.

Figures & tables

Figure 1: Toy Example. Vanilla represents the original flow which is trained to fit into the contour of a cat. Guidance stands for the case where the flow is guided towards two eyes of the cat. Although the guidance successfully steers the trajectory, many trajectories collide with the red yarn ball which serves as the obstacle. Correction means min-norm controller is applied to the former case. While all trajectories are safe, the quality is significantly degraded. Aegis successfully guides most of the trajectories towards the target while maintaining a safe distance from the obstacle.

Figure 2: Conceptual comparison between myopic control and AegisFlow. (a) Myopic Control : A greedy controller driven purely by local target attraction and rigid boundary constraints. It gets trapped sliding jaggedly along the edge of the Unsafe Set and fails to reach the target state. (b) AegisFlow : By explicitly modeling the global cost field, the proposed trajectory is smooth and globally optimal. It proactively avoids the obstacle with an anticipated safety margin and successfully converges to the target. (c) Barrier Cost Landscape : The cost functional used by AegisFlow combines a barrier function to enforce constraints and a reward of the target, balancing constraint satisfaction and target guidance.

Figure 3: Visualization of text-guided image manipulation on CelebA-HQ. The row "+ MNC" shows the results when MNC is applied on OC-Flow.

Method	CLIP $\uparrow$	LPIPS $\downarrow$	ID $\uparrow$
CG + RF [ 13 ]	0.292	0.346	0.643
CG + LDM [ 13 ]	0.298	0.383	0.513
DiffusionCLIP [ 30 ]	0.285	0.398	0.659
StyleCLIP + e4e [ 42 ]	0.267	0.359	0.704
FlowGrad + RF [ 36 ]	0.299	0.302	0.737
OC-Flow [ 56 ]	0.302	0.207	0.732

Table 1: Comparison of AegisFlow with state-of-the-art methods on CelebA-HQ. The best results are in bold . We also include the results of directly applying MNC for reference.

Figure 4: Quantitative Analysis on CelebA-HQ. a. The value of the function $h(x,t)$ at each timestep. The solid lines represent the mean value for the three methods and the shallow bands represent the range of variation. The x-axis is emphasized by a dash line since the forward invariance of $\mathcal{C}_{t}$ requires $h(x,t)\geq 0$ for all $t$ . b. AegisFlow achieves a more favorable balance between text alignment (CLIP) and structure preservation (LPIPS). Connected markers represents different hyperparameter settings (See Appendix D.2 ).

Figure 5: Visualization of path generation process in Maze2D. Red circles represent the obstacles. AegisFlow behaves more proactively to maintain a large margin from the boundary of the safe set in the early stages of generation.

Method	BS1 $\uparrow$	BS2 $\uparrow$	Score $\uparrow$	$\kappa$ $\downarrow$	$a$ $\downarrow$
Diffuser [ 27 ]	-0.825	-0.784	1.572 $\pm$ 0.288	77.04 $\pm$ 4.30	86.68 $\pm$ 3.81
FlowMatcher	-0.324	-0.904	1.632 $\pm$ 0.003	73.51 $\pm$ 1.02	88.45 $\pm$ 0.60
ROS-SafeDiffuser [ 57 ]	0.010	0.010	1.435 $\pm$ 0.502	75.15 $\pm$ 6.67	422.87 $\pm$ 86.70
RES-SafeDiffuser [ 57 ]	0.010	0.010	1.442 $\pm$ 0.451	80.30 $\pm$ 13.06	398.17 $\pm$ 1060.86
TVS-SafeDiffuser [ 57 ]	-0.003	-0.003	1.506 $\pm$ 0.405	78.72 $\pm$ 7.80	124.51 $\pm$ 34.22
SafeFlowMatcher [ 58 ]	0.020	0.041	1.632 $\pm$ 0.003	51.97 $\pm$ 2.55	65.71 $\pm$ 2.45

Table 2: Comparison of AegisFlow with state-of-the-art methods on Maze2D. The best results are in bold . BS1 and BS2 being positive (

\geq 0

) indicates the trajectory is safe with respect to the corresponding constraint.

a\pm b

means

a

is the mean and

b

is the standard deviation over 100 trials.

Figure 6: Qualitative Results for Robotic Manipulation. a. Visualization of the robotic manipulation task. The object is to reach the green line while avoiding collision with the red obstacles. b. Generated trajectories by Flowmatcher. c. Generated trajectories by AegisFlow. The novel test-time constraints are that the robot should not enter the blue regions.

Method	Timesteps $\downarrow$	Goal $\uparrow$	Safe $\uparrow$	Violation $\downarrow$
Diffuser [ 27 ]	76.7 $\pm$ 12.7	1.00	0.07	17.8 $\pm$ 12.1
Flowmatcher	64.2 $\pm$ 9.4	1.00	0.22	14.8 $\pm$ 11.5
DOM [ 22 ]	79.1 $\pm$ 13.9	1.00	0.96	0.1 $\pm$ 0.5
Model-free [ 46 ]	76.1 $\pm$ 12.1	0.99	0.07	18.0 $\pm$ 12.0
DPCC-C [ 47 ]	69.0 $\pm$ 12.9	1.00	0.98	0.0 $\pm$ 0.3
AegisFlow (Ours)	62.6 $\pm$ 2.0	1.00	0.98	0.1 $\pm$ 0.5

Table 3: Comparison of AegisFlow with state-of-the-art methods on Avoiding. The best results are in bold .

a\pm b

means

a

is the mean and

b

is the standard deviation over 100 trials.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

U-Net channels	$(1,4,8)\times 32$
Loss type	L2
Training steps	1M
Steps per epoch	5K
Batch size	64
Learning rate	2e-4
EMA decay	0.995

Appendix

Table 4: Training strategy for the flow matching model in maze navigation.

Dataset	Method	Computation Time (s)
CelebA-HQ	OC-Flow	421.02 $\pm$ 25.56
	OC-Flow + MNC	518.26 $\pm$ 25.54
	AegisFlow	433.81 $\pm$ 25.57
Maze2D	SafeDiffuser	4.78 $\pm$ 0.42
	SafeFlowmatcher	4.21 $\pm$ 0.39
	AegisFlow	44.15 $\pm$ 1.96

Appendix

Table 5: Computational efficiency comparisons.

a\pm b

means

a

is the mean and

b

is the standard deviation over 1000 trials (CelebA-HQ) or 100 trials (Maze2D).

Method	Hyperparameters	CLIP $\uparrow$	LPIPS $\downarrow$	ID $\uparrow$
FlowGrad	+ RF	0.299	0.302	0.737
FlowGrad	+ LDM	0.294	0.298	0.743
OC-Flow	$\alpha=0.6$	0.295	0.119	0.822
	$\alpha=0.7$	0.302	0.207	0.732
	$\alpha=0.8$	0.306	0.192	0.722
	$\alpha=0.9$	0.310	0.244	0.662

Appendix

Table 6: Detailed metrics comparisons for text-guided image manipulation on CelebA-HQ.

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