arXiv:2510.17991cs.LGcs.CV2025-10

过渡匹配比流匹配更优,尤其在模式分离时。

Demystifying Transition Matching: When and Why It Can Beat Flow Matching

  • 用随机更新保持目标协方差,避免确定性方法低估方差。
  • 在有限步数下,过渡匹配的KL散度更低,收敛更快。
  • 适合模式分离明显、方差非零的生成任务,如图像视频生成。

流匹配(FM)是许多先进生成模型的基础,但近期研究表明过渡匹配(TM)可在更少采样步骤下实现更高质量。本文回答了TM何时且为何优于FM。首先,在目标为单峰高斯分布时,我们证明:在有限步数下,TM的KL散度严格低于FM。该优势源于TM中随机差分隐变量更新,能保留目标协方差,而确定性FM会低估。我们进一步分析收敛速率,表明在固定计算预算下,TM收敛更快,确立其在单峰高斯场景中的优势。其次,我们将分析扩展至高斯混合模型,识别出局部单峰区域,在这些区域采样动态近似单峰情形,此时TM可超越FM。近似误差随成分均值间最小距离增大而减小,说明当模式分离良好时,TM更具优势。然而,当目标方差趋近于零时,每个TM更新趋近于FM更新,性能优势消失。综上,我们表明:当目标分布具有分离良好的模式且方差非零时,TM优于FM。我们在高斯分布上进行受控实验验证理论结果,并将对比拓展至真实世界的图像与视频生成任务。

原文摘要 · Abstract (English)

Flow Matching (FM) underpins many state-of-the-art generative models, yet recent results indicate that Transition Matching (TM) can achieve higher quality with fewer sampling steps. This work answers the question of when and why TM outperforms FM. First, when the target is a unimodal Gaussian distribution, we prove that TM attains strictly lower KL divergence than FM for finite number of steps. The improvement arises from stochastic difference latent updates in TM, which preserve target covariance that deterministic FM underestimates. We then characterize convergence rates, showing that TM achieves faster convergence than FM under a fixed compute budget, establishing its advantage in the unimodal Gaussian setting. Second, we extend the analysis to Gaussian mixtures and identify local-unimodality regimes in which the sampling dynamics approximate the unimodal case, where TM can outperform FM. The approximation error decreases as the minimal distance between component means increases, highlighting that TM is favored when the modes are well separated. However, when the target variance approaches zero, each TM update converges to the FM update, and the performance advantage of TM diminishes. In summary, we show that TM outperforms FM when the target distribution has well-separated modes and non-negligible variances. We validate our theoretical results with controlled experiments on Gaussian distributions, and extend the comparison to real-world applications in image and video generation.

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