CounterFlow: Target-Conditioned Flow Matching for Visual Counterfactuals

Paul Sevellec; Elisa Fromont; Romaric Gaudel; Laurence Roze; Paul Viallard; Laetitia Houeix

cs.LGOct 26, 2026

CounterFlow: Target-Conditioned Flow Matching for Visual Counterfactuals

Authors: Paul Sevellec, Elisa Fromont, Romaric Gaudel, Laurence Roze, Paul Viallard, Laetitia Houeix

Organizations: Univ Rennes, CNRS, Inria, IRISA - UMR 6074, F35000 Rennes, France · Stellantis Inc. 78300 Poissy, France · Univ Rennes, INSA Rennes, CNRS, Inria, IRISA - UMR 6074, F35000 Rennes, France

Abstract

In eXplainable AI, counterfactual explanations have gained significant traction by offering users direct, intuitive, and actionable insights into model decisions. We introduce CounterFlow, a novel framework based on Conditional Flow Matching that generates visual counterfactual explanations by directly steering a source image toward a user-specified target class. By leveraging target-conditioned vector fields, CounterFlow identifies highly realistic semantic modifications while requiring substantially lower computational overhead than traditional GAN- or diffusion-based architectures. Empirical evaluations on standard benchmarks demonstrate that CounterFlow achieves state-of-the-art performance in both visual realism and target class switching. By working directly in the raw pixel space, CounterFlow offers a more practical solution for real-world deployment.

Figures & tables

Panel of Figure 1 — Figure 1: Qualitative counterfactual explanations generated by CounterFlow on ( 1(a) ) MNIST and ( 1(b) ) CIFAR10. We show five examples per dataset as source / counterfactual pairs ( source on the left of each pair, the corresponding counterfactual generated by CounterFlow on the right), and we indicate the source $\to$ target class transition above each pair. CounterFlow preserves source-specific style, such as stroke thickness and digit slant on MNIST, or object color and orientation on CIFAR10, modifying only what is needed to reach the target class.

Table 1: (a) Quantitative results and (b) Ablation of the pairing used to train CounterFlow: latent-space nearest neighbor ( Algorithm 1 ) vs. random. Higher conditional validity (CV) is better, while lower FID scores indicate that the generated counterfactuals are closer to the target or source distributions. Lower FLOPs/sample and model size (MS) are preferred for computational efficiency.

Panel of Figure 2 — Figure 2: CounterFlow trajectories for five (MNIST) and six (CIFAR10) samples, from source to target class (labeled for CIFAR10). Border color indicates the classifier’s prediction along the path: red for the source class, green for the target class.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Hyperparameter	MNIST	CIFAR10
Training steps	200,000	400,000
Warmup steps	5,000	5,000
Minibatch size	256	256
Optimizer	Adam	Adam
Learning rate	$1\times 10^{-4}$	$1\times 10^{-4}$
EMA decay	0.9999	0.9999

Appendix

Table 2: Training hyperparameters for MNIST and CIFAR10.

Panel of Figure 3 — Figure 3: Radar comparison of all five metrics from Table 1(a) , per dataset. Each axis is min-max normalized within its dataset so that the outer edge always corresponds to the best value across methods, regardless of whether the underlying metric is originally better when higher or lower. CounterFlow reaches the outer edge on every axis on CIFAR-10 and is competitive or best on most axes on MNIST, whereas baselines tend to excel on a single axis at the expense of others.

Ablated factor	CV $\uparrow$	FID t $\downarrow$	FID s $\downarrow$
$\lambda=0$ (no $\mathcal{L}_{\mathrm{Cla}}$ ) †	68.9	67.64	112.94
$\lambda=0.1$ (default)	100.0	62.54	117.03
$\lambda=0.2$	100.0	66.78	119.77
$\lambda=0.5$	100.0	74.01	121.82
$\lambda=1$ (no $\mathcal{L}_{\mathrm{CFM}}$ ) †	48.9	444.88	406.14

Appendix

Table 3: Effect of the weight

\lambda

of the classification loss

\mathcal{L}_{\mathrm{Cla}}

on CIFAR-10.

Ablated factor	CV $\uparrow$	FID t $\downarrow$	FID s $\downarrow$
$c=(y_{0},y_{1})$ (default)	100.0	62.54	117.03
No context †	8.6	121.72	83.24

Appendix

Table 4: Effect of the context

c

conditioning the velocity field

v_{\theta}

on CIFAR-10.

Explained classifier $f$	Acc.	CV $\uparrow$	FID t $\downarrow$	FID s $\downarrow$
RepVGG-A2 (default)	94.8	100.0	62.54	117.03
RepVGG-A2 w/o input normalization	86.3	100.0	64.03	115.30
Robust PreActResNet-18 ( Gowal et al., 2021 ) †	87.5	83.5	55.72	119.89

Appendix

Table 5: Effect of the explained classifier

f

on CIFAR-10. Accuracy (Acc.) is the test accuracy in % of the explained classifier itself, not a property of the generated counterfactuals.

Figure 4: Additional CounterFlow trajectories on MNIST, from source to target class. Border color indicates the classifier’s prediction along the path: red for the source class, green for the target class, and orange for any other class.

Figure 5: Additional CounterFlow trajectories on CIFAR10, from source to target class. Border color indicates the classifier’s prediction along the path: red for the source class, green for the target class, and orange for any other class.

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CLEAR: Cooperative Latent Flow for Visual Counterfactual Explanations with Accurate Region Preservation

Yan Zeng, Changlu Guo, Oskar Kristoffersen, Anders Nymark Christensen+2

Technical University of Denmark

Counterfactual Explanations Counterfactual Image Generation Explainable Image Classification

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Visual counterfactual explanations (VCEs) should alter a classifier's prediction while remaining realistic and preserving decision-irrelevant content. Image-space methods provide high-quality counterfactuals but are computationally costly, whereas latent-space methods are more efficient but often less faithful. We identify two sources responsible for this gap. First, latent generation recovers a natural sample from a perturbed representation, whereas classifier guidance pushes it toward a target class, so their update directions may oppose. Second, VAE reconstruction can alter regions that should remain unchanged. We introduce CLEAR, a latent Flow Matching framework for VCEs. CLEAR uses Flow Matching's explicit instantaneous velocity as a reference for the generative direction to decompose classifier guidance into cooperative and conflicting components. It preserves the cooperative component and adaptively attenuates only the conflicting one according to conflict strength. We further analyze conflict frequency and strength throughout generation to reveal how classifier guidance interacts with the generative process. CLEAR also dynamically identifies editable regions, constrains latent modifications, and directly preserves factual content outside them to reduce VAE-induced changes. Across five bidirectional tasks on two datasets, CLEAR retains latent-space efficiency while achieving counterfactual quality comparable to or better than strong image-space baselines, with a 2.5x speedup over the strongest baseline. Project page: https://yan-zen9.github.io/CLEAR/

Abstract

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