# CounterFlowNet: From Minimal Changes to Meaningful Counterfactual Explanations

arXiv: https://arxiv.org/abs/2602.17244 · HTML: https://mlsanity.com/paper/2602.17244/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 34 references that are in the map.
- First posted on arXiv 19 Feb 2026.

## Builds on (most cited first, 20 of 20)

- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [European Union regulations on algorithmic decision-making and a "right to explanation"](https://mlsanity.com/paper/1606.08813/) (2016)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019)
- [Biological Sequence Design with GFlowNets](https://mlsanity.com/paper/2203.04115/) (2022)
- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
- [Learning Model-Agnostic Counterfactual Explanations for Tabular Data](https://mlsanity.com/paper/1910.09398/) (2019)
- [Towards Realistic Individual Recourse and Actionable Explanations in Black-Box Decision Making Systems](https://mlsanity.com/paper/1907.09615/) (2019)
- [RGFN: Synthesizable Molecular Generation Using GFlowNets](https://mlsanity.com/paper/2406.08506/) (2024)
- [DAG Matters! GFlowNets Enhanced Explainer For Graph Neural Networks](https://mlsanity.com/paper/2303.02448/) (2023)
- [Counterfactual Plans under Distributional Ambiguity](https://mlsanity.com/paper/2201.12487/) (2022)
- [Probabilistically Plausible Counterfactual Explanations with Normalizing Flows](https://mlsanity.com/paper/2405.17640/) (2024)
- [CeFlow: A Robust and Efficient Counterfactual Explanation Framework for Tabular Data using Normalizing Flows](https://mlsanity.com/paper/2303.14668/) (2023)
- [MCCE: Monte Carlo sampling of realistic counterfactual explanations](https://mlsanity.com/paper/2111.09790/) (2021)
- [Scalable and Cost-Efficient de Novo Template-Based Molecular Generation](https://mlsanity.com/paper/2506.19865/) (2025)
- [DiCoFlex: Model-agnostic diverse counterfactuals with flexible control](https://mlsanity.com/paper/2505.23700/) (2025)

## Abstract (arXiv)

Counterfactual explanations (CFs) provide human-interpretable insights into model's predictions by identifying minimal changes to input features that would alter the model's output. However, existing methods struggle to generate multiple high-quality explanations that (1) affect only a small portion of the features, (2) can be applied to tabular data with heterogeneous features, and (3) are consistent with the user-defined constraints. We propose CounterFlowNet, a generative approach that formulates CF generation as sequential feature modification using conditional Generative Flow Networks (GFlowNet). CounterFlowNet is trained to sample CFs proportionally to a user-specified reward function that can encode key CF desiderata: validity, sparsity, proximity and plausibility, encouraging high-quality explanations. The sequential formulation yields highly sparse edits, while a unified action space seamlessly supports continuous and categorical features. Moreover, actionability constraints, such as immutability and monotonicity of features, can be enforced at inference time via action masking, without retraining. Experiments on eight datasets under two evaluation protocols demonstrate that CounterFlowNet achieves superior trade-offs between validity, sparsity, plausibility, and diversity with full satisfaction of the given constraints.