FlowForget: Data Unlearning in Flow Matching Models via On-Policy Distillation and Preference Optimization

Flow Matching has emerged as an effective paradigm for modern generative modeling and often relies heavily on large-scale training data. Some training samples may later need to be removed for privacy, safety, or copyright reasons. In this paper, we focus on flow matching data unlearning, which aims to remove the influence of specified training samples while preserving overall generative quality. This task faces two key challenges: preserving model utility during forgetting and constructing effective sample-level forgetting signals. Existing methods typically preserve utility with fixed reference targets, which may poorly reflect the model's evolving generation distribution. Moreover, flow matching unlearning largely focuses on concept-level erasure, with limited support for individual-sample removal. To address these challenges, we propose **FlowForget**, an on-policy distillation and preference optimization framework for flow matching data unlearning. **FlowForget** transforms the deterministic flow ordinary differential equation into a stochastic process that preserves its marginal distributions, yielding non-degenerate transition policies for policy matching during generation. It then performs teacher-guided on-policy distillation along the model's current trajectories to preserve generative behavior using retained data. Furthermore, **FlowForget** evaluates sampled generations with a joint reward and applies group relative policy optimization over stochastic trajectories to obtain adaptive forgetting signals. Extensive experiments on real-world datasets demonstrate that **FlowForget** achieves effective data unlearning while maintaining generative quality.