Coupled Guidance for Flow Matching

Mateo Clémente; Léo Maxime Brunswic; Rui Heng Yang; Amir Rasouli

cs.LGOct 29, 2026

Coupled Guidance for Flow Matching

Authors: Mateo Clémente, Léo Maxime Brunswic, Rui Heng Yang, Amir Rasouli

Organizations: Huawei

Abstract

Guidance methods are essential tools for steering the generation process in diffusion models, improving the generalizability of stochastic robotic controllers and enabling high-quality controlled image synthesis. Despite strong parallels between flow-matching and diffusion, integrating guidance into flow-matching models remains quite challenging. Recent work has proposed general guidance frameworks for flow-matching, however, they are direct adaptations of diffusion guidance methods and can prove unstable. In this work, we conduct a theoretical analysis of guidance in flow-matching and show that a naive translation of diffusion-based guidance to flow-matching breaks the coupling distribution used during training, resulting in weaker control over sampling accuracy. Building on this insight, we propose Coupled Guidance, a flow-matching-specific guidance mechanism derived from a geometric perspective that leverages the coupling structure inherent to flow-matching training. To validate the effectiveness of our approach, we conduct extensive experimentation on a custom robotic collision avoidance task using ManiSkill3, four robotic dexterous manipulation tasks from the Adroit benchmark, and three image generation tasks, namely inpainting, super-resolution, and deblurring, using the ImageNet-128 and CelebA-HQ-256 datasets. Our findings show that our framework improves sample quality and guidance stability across all tasks, without imposing any additional overhead.

Figures & tables

Figure 1: Qualitative examples of image reconstructions for noiseless inpainting, deblurring, and super-resolution, comparing naive $\Pi$ GDM , $\Pi$ GDM + , and our coupled guidance method.

Table 2

$\alpha\backslash\beta$	-1	0	1
0	73	21	17
1	81	77	36

Table 2: Collision avoidance success rates (%) for all

(\alpha,\beta)

couples, over 256 environment seeds.

Panel of Figure 2 — Figure 2: Experimental setups for robotics tasks. From left to right: Maniskill PickCube, Adroit Door, Hammer, Relocate, and Pen.

Panel of Figure 3 — Figure 3: Performance of $\Pi$ GDM on Adroit tasks given different sparsity cutoffs. Runs using coupled guidance are used directly without a unit guidance scale $s=1$ . The blue lines each represent the performance of naive guidance for different guidance scalings $s$ .

Panel of Figure 4 — Figure 4: LPIPS scores for $\Pi$ GDM , (first row) and $\Pi$ GDM + (second row) on super-resolution

Figure 5: Evolution of $\partial\widehat{x}_{1}/\partial x_{t}$ ’s contribution to the guidance norm for the CelebA-HQ-256 superresolution task through the $\Pi$ GDM inference process.

Appendix figures & tables20 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 6: Sparsity tests for all Adroit tasks using

\Pi

GDM + : the cutoff represents the proportion of guided coordinates. Different shades of blue represent different tunings of the guidance scale for the naive guidance runs (

\beta=1

)

Figure 7: Sparsity tests for all Adroit tasks using

\Pi

GDM : the cutoffs represent the proportion of guided coordinates. Different shades of blue represent different tunings of the guidance scale for the naive guidance runs (

\beta=1

)

		Naive		Coupled
Task	Metric	PiGDM	PiGDM+	PiGDM	PiGDM+
Inpainting	FID $\downarrow$	54.3	7.5	20.7	7.5
	LPIPS $\downarrow$	0.184	0.041	0.100	0.041
	PSNR $\uparrow$	20.5	29.3	30.1	29.1
	SSIM $\uparrow$	0.873	0.953	0.927	0.953
Deblurring	FID $\downarrow$	54.0	22.7	33.0	22.7

Appendix

Table 3: Comparison of naive vs. coupled guidance across methods and tasks on CelebA-HQ-256.

		Naive		Coupled
Task	Metric	$\Pi$ GDM	$\Pi$ GDM+	$\Pi$ GDM	$\Pi$ GDM+
Inpainting	FID $\downarrow$	13.0	10.5	8.8	11.3
	LPIPS $\downarrow$	0.106	0.086	0.092	0.088
	PSNR $\uparrow$	20.4	20.5	23.4	20.6
	SSIM $\uparrow$	0.907	0.911	0.908	0.909
Deblurring	FID $\downarrow$	58.6	1.6	16.6	1.2

Appendix

Table 4: Comparison of naive vs. coupled guidance across methods and tasks on ImageNet (CFM).

Panel of Figure 8 — Figure 8: Sample fidelity using different tuning scales and $\beta$ values for deblurring, superresolution and inpainting (left to right). First row shows the LPIPS scores for $\Pi$ GDM , second row shows the performance of $\Pi$ GDM +

Panel of Figure 9 — Figure 9: Sample fidelity using different tuning scales and $\beta$ values for deblurring, superresolution and inpainting (left to right). First row shows the PSNR scores for $\Pi$ GDM , second row shows the performance of $\Pi$ GDM +

Panel of Figure 10 — Figure 10: Sample fidelity using different tuning scales and $\beta$ values for deblurring, superresolution and inpainting (left to right). First row shows the SSIM scores for $\Pi$ GDM , second row shows the performance of $\Pi$ GDM +

Panel of Figure 11 — Figure 11: Sample fidelity using different tuning scales and $\beta$ values for deblurring, superresolution and inpainting (left to right). First row shows the FID scores for $\Pi$ GDM , second row shows the performance of $\Pi$ GDM +

Figure 12: $\widehat{x}_{1}$ predictions using $\Pi$ GDM for the first 10 steps of deblurring showing the convergence of the guided process for $\beta\in[1,0.75,0.5,0.25,0]$ (from top to bottom)

Figure 13: $\widehat{x}_{1}$ predictions using $\Pi$ GDM for the first 10 steps of inpainting showing the convergence of the guided process for $\beta\in[1,0.75,0.5,0.25,0]$ (from top to bottom)

Figure 14: $\widehat{x}_{1}$ predictions using $\Pi$ GDM for the first 10 steps of superresolution showing the convergence of the guided process for $\beta\in[1,0.75,0.5,0.25,0]$ (from top to bottom)

Figure 15: $\widehat{x}_{1}$ predictions using $\Pi$ GDM + for the first 10 steps of deblurring showing the convergence of the guided process for $\beta\in[1,0.75,0.5,0.25,0]$ (from top to bottom)

Figure 16: $\widehat{x}_{1}$ predictions using $\Pi$ GDM + for the first 10 steps of inpainting showing the convergence of the guided process for $\beta\in[1,0.75,0.5,0.25,0]$ (from top to bottom)

Figure 17: $\widehat{x}_{1}$ predictions using $\Pi$ GDM + for the first 10 steps of superresolution showing the convergence of the guided process for $\beta\in[1,0.75,0.5,0.25,0]$ (from top to bottom)

Figure 18: Final samples for deblurring using $\Pi$ GDM with $\beta\in[1,0.75,0.5,0.25,0]$ (from left to right)

Figure 19: Final samples for inpainting using $\Pi$ GDM with $\beta\in[1,0.75,0.5,0.25,0]$ (from left to right)

Figure 20: Final samples for superresolution using $\Pi$ GDM with $\beta\in[1,0.75,0.5,0.25,0]$ (from left to right)

Figure 21: Final samples for deblurring using $\Pi$ GDM + with $\beta\in[1,0.75,0.5,0.25,0]$ (from left to right)

Figure 22: Final samples for inpainting using $\Pi$ GDM + with $\beta\in[1,0.75,0.5,0.25,0]$ (from left to right)

Figure 23: Final samples for superresolution using $\Pi$ GDM + with $\beta\in[1,0.75,0.5,0.25,0]$ (from left to right)

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Inference-time guided sampling steers state-of-the-art diffusion and flow models without fine-tuning by interpreting the generation process as a controllable trajectory. This provides a simple and flexible way to inject external constraints (e.g., cost functions or pre-trained verifiers) for controlled generation. However, existing methods often fail when composing multiple constraints simultaneously, which leads to deviations from the true data manifold. In this work, we identify root causes of this off-manifold drift and find that the approximation error scales severely with gradient misalignment. Building on these findings, we propose Conflict-Aware Additive Guidance (

g^\text{car}

), a lightweight and learnable method, which actively rectifies off-manifold drift by dynamically detecting and resolving gradient conflicts. We validate

g^\text{car}

across diverse domains, ranging from synthetic datasets and image editing to generative decision-making for planning and control. Our results demonstrate that

g^\text{car}

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