提出反向流匹配方法,提升图像异常检测精度与推理速度。
Time-reversed Flow Matching with Worst Transport in High-dimensional Latent Space for Image Anomaly Detection
- 采用反向流匹配,用密度代理替代精确似然计算。
- 在5个数据集上达到单尺度流模型最佳性能,每张图仅需6.7毫秒。
- 适合追求高效高精度异常检测的工业场景应用。
基于似然的深度生成模型广泛用于图像异常检测(IAD),尤其是归一化流,但其严格的可逆架构常限制大规模数据下的可扩展性。尽管时间参数化流匹配(FM)作为可扩展替代方案,但在IAD中仍因雅可比行列式估计成本过高而面临计算挑战。本文提出反向流匹配(rFM),将目标从精确似然计算转为通过密度代理评估目标域规则性。我们揭示该范式存在两大理论瓶颈:一是反向向量场在初始时间边界出现非Lipschitz奇点,导致估计误差爆炸;二是高维高斯流形中的测度集中效应引发结构化不规则性,形成向心势场(CPF),使轨迹偏离最优传输(OT)路径。我们识别出FM与rFM之间的内在双重性。为此,提出局部最坏传输流匹配(WT-Flow),放大rFM中的CPF以缓解初始奇点问题,同时通过密度代理规避精确分布变换需求。在五个数据集上的实验表明,WT-Flow在单尺度流模型中达到当前最优性能,并在多尺度方法中表现具有竞争力。此外,该框架支持优越的一步推断,实现每图像仅6.7毫秒的流延迟。代码已开源于https://github.com/lil-wayne-0319/fmad。
原文摘要 · Abstract (English)
Likelihood-based deep generative models have been widely investigated for Image Anomaly Detection (IAD), particularly Normalizing Flows, yet their strict architectural invertibility needs often constrain scalability, particularly in large-scale data regimes. Although time-parameterized Flow Matching (FM) serves as a scalable alternative, it remains computationally challenging in IAD due to the prohibitive costs of Jacobian-trace estimation. This paper proposes time-reversed Flow Matching (rFM), which shifts the objective from exact likelihood computation to evaluating target-domain regularity through density proxy estimation. We uncover two fundamental theoretical bottlenecks in this paradigm: first, the reversed vector field exhibits a non-Lipschitz singularity at the initial temporal boundary, precipitating explosive estimation errors. Second, the concentration of measure in high-dimensional Gaussian manifolds induces structured irregularities, giving rise to a Centripetal Potential Field (CPF) that steers trajectories away from Optimal Transport (OT) paths. We identify these observations as the inherent dualities between FM and rFM. To address these issues, we introduce local Worst Transport Flow matching (WT-Flow), which amplifies the observed CPF of rFM to mitigate the initial singularity while circumventing the need for exact distribution transformations via density proxy. Experiments on five datasets demonstrate that WT-Flow achieves state-of-the-art performance among single-scale flow-based methods, and competitive performance against leading multi-scale approaches. Furthermore, the proposed framework enables superior one-step inference, achieving a per-image flow latency of only 6.7 ms. Our code is available on https://github.com/lil-wayne-0319/fmad.
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