[Submitted on 31 Jan 2026 (
[v1](https://arxiv.org/abs/2602.00797v1)), last revised 7 Jun 2026 (this version, v3)]# Title:Zero-Flow Encoders
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Abstract:Flow-based methods have achieved significant success in various generative modeling tasks, capturing nuanced details within complex data distributions. However, few existing works have exploited this unique capability to resolve fine-grained structural details beyond generation tasks. This paper presents a flow-inspired framework for representation learning. First, we demonstrate that a rectified flow trained using independent coupling is zero everywhere at $t=0.5$ if and only if the source and target distributions are identical. We term this property the \emph{zero-flow criterion}. Second, we show that this criterion can certify conditional independence, thereby extracting \emph{sufficient information} from the data. Third, we translate this criterion into a tractable, simulation-free loss function that enables learning amortized Markov blankets in graphical models and latent representations in self-supervised learning tasks. Experiments on both simulated and real-world datasets demonstrate the effectiveness of our approach. The code reproducing our experiments can be found at:[this https URL].
Submission history #
From: Yakun Wang [[view email](/show-email/039a3d78/2602.00797)]
**Sat, 31 Jan 2026 16:11:01 UTC (6,198 KB)**
[[v1]](/abs/2602.00797v1)**Thu, 4 Jun 2026 16:53:55 UTC (3,466 KB)**
[[v2]](/abs/2602.00797v2)**[v3]** Sun, 7 Jun 2026 16:59:20 UTC (3,466 KB)
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