Title: Scalable, Explainable and Provably Robust Anomaly Detection with One-Step Flow Matching
Venue: NeurIPS 2025
Accepted: yes
Keywords: Anomaly Detection

Outlier Detection
Abstract: We introduce Time-Conditioned Contraction Matching (TCCM), a novel method for semi-supervised anomaly detection in tabular data. TCCM is inspired by flow matching, a recent generative modeling framework that learns velocity fields between probability distributions and has shown strong performance compared to diffusion models and generative adversarial networks. Instead of directly applying flow matching as originally formulated, TCCM builds on its core idea—learning velocity fields between distributions—but simplifies the framework by predicting a time-conditioned contraction vector toward a fixed target (the origin) at each sampled time step. This design offers three key advantages: (1) a lightweight and scalable training objective that removes the need for solving ordinary differential equations during training and inference; (2) an efficient scoring strategy called one time-step deviation, which quantifies deviation from expected contraction behavior in a single forward pass, addressing the inference bottleneck of existing continuous-time models such as DTE (a diffusion-based model with leading anomaly detection accuracy but heavy inference cost);
and (3) explainability and provable robustness, as the learned velocity field operates directly in input space, making the anomaly score inherently feature-wise attributable; moreover, the score function is Lipschitz-continuous with respect to the input, providing theoretical guarantees under small perturbations. Extensive experiments on the ADBench benchmark show that TCCM strikes a favorable balance between detection accuracy and inference cost, outperforming state-of-the-art methods—especially on high-dimensional and large-scale datasets. The source code is provided at https://github.com/ZhongLIFR/TCCM-NIPS.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a novel semi-supervised AD method for tabular data using the concept of flowing matching. Specifically, the author uses a neural network to predict the time-dependent velocity field in the transformation between normal data distribution and a degenerate Dirac distribution at the origin. The method is evaluated on the popular benchmark ADbench, and the  method outperforms all baselines in the average rank, also the authors provides several theoretical guarantees for the method and detailed experimental results for ablation studies.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:**\n\n1. The authors provide complete experimental results. 2. The method demonstrates good experimental performance on a wide range of datasets. 3. The paper is easy to follow and well written.\n\n**Weaknesses:**\n1. In the limitations of existing studies, the authors mention that \"rely on restrictive architectural constraints (e.g., no biases, bounded\nactivations) to avoid representation collapse\". For TCCM, i think representation or model collapse could also happen, e.g., consider the neural network is a one-layer MLP, $f_θ([\\mathbf{z}; \\mathrm{Embed}(t)])=[-I,\\mathbf{0}][\\mathbf{z}; \\mathrm{Embed}(t)]^T=-\\mathbf{z}$. In this case, the loss attains minimal but the model can not identify normal data and anomalous data, and it seems that this model collapse is not mentioned and solved in the paper.\n\n2. Usually, in flow matching or score matching, the points in the original distribution and points in the target distribution correspond one-to-one. But in the paper authors use \"a degenerate Dirac distribution at the origin\" as the target distribution, which contains only one point, indicating a relationship of one-to-many.  This does not make sense to me.\n\n3. In the training process of TCCM, for different timestep $t$, $\\mathbf{z}_t=\\mathbf{z}_0$, and this is different from original flow matching. The only change in $\\tilde{\\mathbf{z}}_t$ is the time embedding. If  $\\mathbf{z}_t$ does not change for different $t$, then it is not a \"flow\".  In my understanding, the trajectory is a straight line and you should sample from the line $\\mathbf{z}_t=\\frac{\\mathbf{z}-\\mathbf{0}}{t}$ to train TCCM. For this reason, TCCM is more like an AE on augmented data combining self-supervised learning and auto-encoder, which is not novel.\n\nQUESTIONS:\n**Method**:\nSee weakness. If the authors address my concerns properly, i will raise my score.\n\n**Experimental Results**:\n\n1. In the experimental results of the paper, the performance of $k$NN is much worse than most of methods. However, in [1],  following the same experimental setting, $k$NN is almost the most powerful semi-supervised AD method. Why the perfromance of $k$NN is so different in the paper? Also, there are several recent AD methods based on generative models and AE to be mentioned and compared, e.g. [2] [3] [4].\n\n[1] Livernoche, Victor, et al. \"On diffusion modeling for anomaly detection.\" arXiv preprint arXiv:2305.18593 (2023).\n\n[2] Liu et al. Unsupervised Anomaly Detection by Robust Density Estimation, AAAI 2022\n\n[3] Rozner et al. Anomaly Detection with Variance Stabilized Density Estimation, UAI 2024 \n\n[4] Lindenbaum, et al. Transductive and inductive outlier detection with robust autoencoders. UAI 2024 \n\n\n2. In the time comparison part, the authors compare TCCM with two non-parametric methods: KDE and DTENP, and LUNAR which requires graph converting. Then the authors claim that \"TCCM achieves considerably faster inference than most deep learning baselines\". I think this is quite unfair since the time complexity of the $3$ methods is at least $\\mathcal{O}(n^2d)$ and there are many faster deep learning methods like auto-encoder, DeepSVDD, MCM and so on.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper concerns an unsupervised anomaly detection problem (the authors call it semi-supervised), where a training set consists only of normal instances and the model is trained to detect anomalies by defining a score. The authors propose a model based on flow matching that predicts a contracting vector towards the origin at each time step. The model seems to be intuitive and is demonstrated to be competitive with related approaches. The evaluation was performed on well established benchmark. Additionally the authors claim that the model is efficient from the computational point of view, intepretable, and robust (the authors give theoretical statement for this).\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. The experimental results presented in the main paper show that the method outperforms almost all methods. The evaluation uses 47 datasets and more than 30 algorithms taken in part from ADBench.\n2. The method simplifies a standard flow matching model to directly describe the underlying problem. In consequence, no irrelevant distribution modeling is performed and the method focuses on the anomaly detection problem.\n3. The authors provide theoretical analysis certifying the robustness and giving the insight into the score function behavior.\n\nWeaknesses:\n1. The interpretability experiment is not convincing at all. The authors show two examples on MNIST, which do not support the claim \"the model highlights the additional horizontal stroke that distinguishes 7 from 1\". The model also highlight digit borders and the bottom. Nevertheless, the authors are required to show this propoerty on more examples, e.g. user-study.\n2. The computation efficiency of the method on inference compared to 3 best performing baselines is ok. The question is how the method compares with all 30 algorithms? Moreover, Fig 5 show that the best performing DTEN method is significantly faster at training, which is in contrast to authors claim. Fig 6 show that the training + inference time of both methods is comparable.\n\nQUESTIONS:\nThe authors use claims which are not supported in the paper. The method does not seem to be explainable no more efficient than the other methods. In consequence, the title and main contributions are incorrect. The results are do not support the claims are hidden in appendix. I do not see why the method is called semi-supervised since is does not use labeled samples in training.\n\nThe authors say that the method is designed for tabular data. Tabular data is specific. It consists of mixed-type features, have high extreme values, etc. I do not see where the authors address this data type is a special way.\n\nThe authors say \"Despite its recent success in generative modeling, flow matching has not been explored for anomaly detection, to the best of our knowledge\". I do not think it is a good motivation for the paper.\n\nThe authors report ROC curves in their experiments which do not require setting a threshold whether the sample is normal or abnormal. F1 and Acc are equally popular but the method needs to find a threshold. Can we find a natural threshlod in this method? I would like to see experiment on that. \n\nI like the experiment presented in Fig 10. I think this should be in the main paper (instead of interpretability experiment). Additionally, the authors should show how their method compares with baselines in this setting. Without it, it is difficult to see the advantage.\n\nThe Table 3  present incorrect information - DTE is as scalable as the proposed method. Moreover, the method is not interpretable/explainable.\n\nI am not sure whether eq 4 is correct. Looking at the paper https://arxiv.org/pdf/2209.03003 is seems that instead of \"z\" we should have \"tz\" or \"(1-t)z\". Otherwise the model will return constant identity function (ignoring t).\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors present a novel approach to anomaly detection in tabular data coined TCCM, leveraging a flow matching framework to learn a time-conditioned contraction field that guides samples towards a degenerate target distribution.  This work is inspired by flow matching, but also deviates from it with a simpler more efficient method dedicated to anomaly detection. Especially, no differential equation is involved in the process. The method is inherently interpretable and provably robust, with a Lipschitz-continuous anomaly score that provides theoretical guarantees under small perturbations. The paper provides an extensive experimental evaluation of TCCM across 47 benchmark datasets and against 45 anomaly detectors, demonstrating its effectiveness and robustness. Also, TCCM is shown to be quite highly efficient and scalable, outperforming state-of-the-art methods in terms of detection accuracy and inference speed.\n\nSTRENGTHS AND WEAKNESSES:\n#### Strengths\n\n- The paper is very clearly written and organized.\n- The set of experiments to support the claims is extensive, whether by the number of datasets and contenders, or by the study of ablation, contamination, time embeddings, performance (inference time). \n- Especially the AUROC and AUPRC are reported with mean and std over 5 runs\n- Code is published for replaying the experiments\n- Scalability: TCCM achieves state-of-the-art performance on large-scale and high-dimensional datasets (up to those available in ADBench), demonstrating its ability to handle complex data distributions.\n- Explainability: The method provides feature-level importance scores, enabling interpretable diagnosis and supporting the identification of key contributing factors to anomalies.\n- Robustness: TCCM is theoretically justified and empirically validated to be robust under the GMM-to-GMM shift setting, ensuring reliable anomaly detection in the presence of distributional shifts.\n- Efficiency: The approach requires no adversarial training, trajectory simulation, or density modeling, making it more efficient and scalable than existing generative-based anomaly detection methods.\nAll in all, the model provides a good balance between simplicity - efficiency and performance.\n\n#### Weaknesses\n\n- The architecture is fixed as MLP(2 x 256 ReLU) and the hyperparameter of attention is the number of epochs for training. The reference of Li et al. (2025b) is given for the number of epochs. However, the hyperparameters are hardcoded in the provided code. So it is not clear how they have been determined. It would be helpful to know how well TCCM has converged in each case.\n\nQUESTIONS:\n- How the hyperparameters have been fixed? What is the sensitivity to them?\n- How does the model extrapolate to 50/50 classification? (OK, not anymore AD, but could have been discussed)\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes a novel anomaly detection method (TCCM) inspired by flow-matching techniques.\nThe core idea of TCCM is to learn a velocity field that contracts normal datapoints towards the origin.\nThe key assumption is that, during inference, the normal data will be \"squashed\" near the origin, while anomalies will be dispersed elsewhere, thus making them more distinguishable.\nThe paper provides proofs (Appendix C.2) and an extensive experimental evaluation (Section5,  Appendix D) to validate the model against the existing SOTA (Appendix B.2).\n\nSTRENGTHS AND WEAKNESSES:\nAfter a careful read, I believe the strengths of this paper greatly outweigh its weaknesses.\nI am giving a lower confidence score because I am not familiar with the related work.\n\n\n## S1 - Simplicity\nTCCM is conceptually straightforward: it contracts normal data to the origin while dispersing anomalies. This simplicity is a major strength, as it makes the method intuitive, (potentially) easy to implement, and it allows to get strong theoretical guarantees (with some caveats, see W1). Yet, TCCM achieves SOTA performance. \n\n## S2 - Extensive evaluation\nThe experimental evaluation is comprehensive and rigorous, considering a wide range of datasets and baselines. \n\n## S3 - Clarity\nThe paper is exceptionally well-written: clear, detailed, and easy to follow. \nThe presentation is well-structured and the figures informative, in particular Figure 1. \n\n## W1 - Assumed mismatch for anomalies\nOne major theoretical claim (Proposition 2) relies on the assumption that the learned velocity field is mismatched for anomalies (L1208, 1230). \nHowever, this point is stated without formal or experimental justification, nor is it clearly indicated as an assumption of the propositions---L1222 does include it as a *result* of the theorem, but the proof relies on the assumption made on L1230.\n\nQUESTIONS:\nMajor points:\nSee Weaknesses.\n\nSpelling and notation:\n- L131: I find the notation somewhat ambiguous, as $\\mathbf x$ indicates both a vectors (as on L135) and random vectors (as in (4)).\n- L242 (and elsewhere): Sometimes $$||\\cdot||$ has a pedix, sometimes it doesn't. \n\nOpen points for discussion:\n- The authors refer to TCCM as a deep method (L53, L1270), yet Appendix B.3 reports that its architecture is in fact a 3-layer MLP. As the authors acknowledge in the limitations (Appendix D.6), this choice likely trades efficacy for efficiency (potentially explaining the vastly superior speed of TCCM). My point is: why should one consider TCCM a deep method?\n- What if the model learned to contract normal data to another point (e.g., the mean of normal data)?\n\nLIMITATIONS:\nDiscussed in Appendix D.6.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 4, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors propose Time-Conditioned Contraction Matching (TCCM), a method for semi-supervised anomaly detection in tabular data. TCCM avoids adversarial training, trajectory simulation, and density modeling—offering a lightweight yet expressive alternative to existing generative approaches. Evaluated on the ADBench benchmark, TCCM outperforms 44 classical and deep-learning baselines in terms of both AUROC and AUPRC, while achieving significantly faster inference than the strongest diffusion-based competitor. It also provides feature-level interpretability through its learned vector field. Theoretical analysis supports the Lipschitz continuity and discriminative capability of the scoring function. Overall, the method presents itself as a highly effective, scalable, interpretable, and robust solution for large-scale anomaly detection.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n\n1. The authors conduct extensive empirical evaluations, comparing TCCM against a wide range of baseline methods.\n\n2. The evaluation includes multiple datasets and baselines, demonstrating consistent performance improvements.\n\n3. The paper is well written with a good structure. \n\n\nWeaknesses\n\n1. The core idea of the paper appears to be a direct application of Flow Matching. The results, while strong, may not offer substantial novelty.\n\n2. The theoretical analysis is somewhat limited, as it focuses on specific distributions (e.g., Gaussian and Gaussian Mixture Models), which may restrict its generalizability.\n\nQUESTIONS:\n1. Compared to traditional Flow Matching, the proposed training objective removes the need for sampling from a noise distribution. What are the concrete advantages of this modification? Could the original Flow Matching framework be directly applied to anomaly detection, and how would it compare?\n\n2. While a scalability study is included, the datasets used are not extremely large. On what basis is the method claimed to be scalable for very large-scale scenarios?\n\n3. The paper highlights feature-level interpretability. If the method does not provide additional or actionable insights beyond the scoring function, how strong is its claim of being explainable?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-02"}