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arxiv: 2305.18593 · v3 · submitted 2023-05-29 · 💻 cs.LG · cs.AI

On Diffusion Modeling for Anomaly Detection

Victor Livernoche , Vineet Jain , Yashar Hezaveh , Siamak Ravanbakhsh This is my paper

Pith reviewed 2026-05-24 08:41 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords anomaly detectiondiffusion modelsDDPMDTEunsupervised anomaly detectionsemi-supervised anomaly detectiondensity estimation
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The pith

Diffusion Time Estimation simplifies DDPM into a fast anomaly scorer using diffusion time distribution

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines diffusion models as density estimators for anomaly detection in unsupervised and semi-supervised regimes. Standard DDPM performs well on benchmarks but runs slowly, which leads the authors to derive a simpler Diffusion Time Estimation approach. DTE computes an analytical density over the diffusion time required for a given input and treats the mode or mean of that density as the anomaly score. A neural network approximates the density to keep inference cheap. Experiments on the ADBench benchmark show that diffusion methods remain competitive overall, with DTE delivering the same or better accuracy at orders-of-magnitude lower cost.

Core claim

By simplifying DDPM for anomaly detection the authors obtain an analytical expression for the density over diffusion time; a neural network then estimates this density so that its mode or mean can be used directly as an anomaly score. On ADBench this score yields competitive detection performance in both unsupervised and semi-supervised settings while running far faster than full DDPM sampling.

What carries the argument

Diffusion Time Estimation (DTE): the derived density over diffusion time for an input, whose mode or mean supplies the anomaly score

If this is right

  • Diffusion-based detectors are competitive with existing methods for both unsupervised and semi-supervised anomaly detection.
  • DTE inference is orders of magnitude faster than DDPM while matching or exceeding its benchmark scores.
  • Diffusion modeling therefore supplies a practical, scalable route to anomaly detection.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The analytical density derived for DTE may allow closed-form analysis of how diffusion steps separate normal from anomalous points.
  • DTE could be paired with other generative backbones that admit a diffusion-time interpretation.

Load-bearing premise

The mode or mean of the estimated distribution over diffusion time reliably flags anomalies for inputs drawn from the training distribution.

What would settle it

A result on ADBench in which DTE anomaly scores do not rank true anomalies above normal points or in which DTE inference time is not orders of magnitude below DDPM would refute the central performance claim.

Figures

Figures reproduced from arXiv: 2305.18593 by Siamak Ravanbakhsh, Victor Livernoche, Vineet Jain, Yashar Hezaveh.

Figure 1
Figure 1. Figure 1: Average inference time vs. aver￾age AUC ROC for all 57 ADBench datasets in the semi-supervised setting. Lower right is bet￾ter (DTE Categorical). Colour scheme: red (diffusion-based), green (deep learning), blue (classical). More precisely, we estimate the posterior distri￾bution of diffusion time (or noise variance) for a given input. This estimated distribution serves as a guide for identifying anomalies… view at source ↗
Figure 2
Figure 2. Figure 2: DDPM and DTE on a toy dataset shown in (a). (b) shows the Gaussian density function [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Posterior timestep distribution p(σ 2 t |xs), where xs is produced using diffusion with dif￾ferent time steps s ∈ {1, . . . , T}, averaged over the vertebral dataset. (a) shows the analytical distribution computed by placing Gaussian distributions of different variances at each point in the dataset, and (b) shows the inverse Gamma distribution with scale parameter value depending on the average distance to… view at source ↗
Figure 4
Figure 4. Figure 4: Predicted diffusion time against ground truth diffusion time for Gaussian model ( [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: AUC ROC means and standard deviations on the 57 datasets from ADBench over five [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Average AUC ROC over the 57 ADBench datasets for different reconstruction timesteps of the DDPM model. 0 10 20 30 40 50 Number for bins 0.50 0.55 0.60 0.65 0.70 0.75 0.80 Average AUC ROC Unsupervised Semi-supervised [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 9
Figure 9. Figure 9: Standard deviations versus timestep for different values of the maximum timestep T. Maximum timestep in DTE We study the effect of changing the maximum timestep in the noising diffusion process. As seen in [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 8
Figure 8. Figure 8: Average AUC ROC over the 57 ADBench datasets for different maximum timestep T for [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: Interpretability in DTE (first row) and DDPM (second row) on MNIST. Visual interpre￾tation of a gray patch anomaly on an MNIST im￾age using the categorical diffusion model with a simple convolution network on the first row and a DDPM on the second for comparison. a) original anomalous image, b) the denoised version using gradient descent c) difference between the origi￾nal and the denoised image, d) visua… view at source ↗
Figure 11
Figure 11. Figure 11: Posterior timestep distribution p(σ 2 t |xs), where xs is produced using diffusion with different time steps s ∈ {1, . . . , T}, averaged over the vertebral dataset. (a) shows the analytical distribution computed by placing Gaussian distributions of different variances at each point in the dataset, (b) shows the inverse Gamma distribution with scale parameter value depending on the average distance to the… view at source ↗
Figure 12
Figure 12. Figure 12: Mean training and inference time on the 57 datasets from ADBench over five different [PITH_FULL_IMAGE:figures/full_fig_p021_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: F1 score and AUC PR means and standard deviations on the 57 datasets from ADBench [PITH_FULL_IMAGE:figures/full_fig_p023_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: F1 score and AUC PR means and standard deviations on the 57 datasets from ADBench [PITH_FULL_IMAGE:figures/full_fig_p025_14.png] view at source ↗
read the original abstract

Known for their impressive performance in generative modeling, diffusion models are attractive candidates for density-based anomaly detection. This paper investigates different variations of diffusion modeling for unsupervised and semi-supervised anomaly detection. In particular, we find that Denoising Diffusion Probability Models (DDPM) are performant on anomaly detection benchmarks yet computationally expensive. By simplifying DDPM in application to anomaly detection, we are naturally led to an alternative approach called Diffusion Time Estimation (DTE). DTE estimates the distribution over diffusion time for a given input and uses the mode or mean of this distribution as the anomaly score. We derive an analytical form for this density and leverage a deep neural network to improve inference efficiency. Through empirical evaluations on the ADBench benchmark, we demonstrate that all diffusion-based anomaly detection methods perform competitively for both semi-supervised and unsupervised settings. Notably, DTE achieves orders of magnitude faster inference time than DDPM, while outperforming it on this benchmark. These results establish diffusion-based anomaly detection as a scalable alternative to traditional methods and recent deep-learning techniques for standard unsupervised and semi-supervised anomaly detection settings.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates the use of diffusion models for unsupervised and semi-supervised anomaly detection. It shows that DDPM achieves competitive results on the ADBench benchmark but is computationally expensive; it then proposes Diffusion Time Estimation (DTE), which derives an analytical density over diffusion time for a given input and uses the mode or mean of that distribution as the anomaly score, with a neural network to enable efficient inference. Empirical results indicate that diffusion-based methods (including DTE) perform competitively in both settings, with DTE achieving orders-of-magnitude faster inference while outperforming DDPM.

Significance. If the benchmark results hold under standard evaluation protocols, the work provides evidence that diffusion models can serve as a practical, scalable alternative for anomaly detection, with DTE's efficiency advantage being a concrete contribution. The explicit analytical derivation of the time-density and its empirical validation on a public benchmark (ADBench) are strengths that support reproducibility.

major comments (2)
  1. [Experiments section (ADBench results)] Experiments section (ADBench results): the outperformance of DTE over DDPM is load-bearing for the central empirical claim, yet the manuscript does not report whether hyperparameter search budgets and data splits were held identical across all compared methods; without this, the speed/accuracy advantage cannot be isolated from implementation differences.
  2. [DTE derivation] DTE derivation: the mapping from the estimated time distribution to the final anomaly score (mode or mean) is presented as a simplification that works in practice, but the paper provides no ablation showing that alternative statistics (e.g., variance or entropy) yield materially worse detection; this choice is therefore not yet shown to be robust.
minor comments (2)
  1. Notation for the analytical density p(t|x) should be introduced once in the main text with a clear reference to the appendix derivation rather than appearing only in the latter.
  2. Figure captions for runtime comparisons should state the hardware platform and batch size used, to allow direct replication of the reported speed-up.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and recommendation for minor revision. We address the two major comments below.

read point-by-point responses

  1. Referee: Experiments section (ADBench results): the outperformance of DTE over DDPM is load-bearing for the central empirical claim, yet the manuscript does not report whether hyperparameter search budgets and data splits were held identical across all compared methods; without this, the speed/accuracy advantage cannot be isolated from implementation differences.

    Authors: We agree that explicit confirmation of identical experimental conditions is necessary to isolate methodological differences. The original experiments followed ADBench's provided data splits and applied comparable hyperparameter tuning effort (grid/random search within similar compute limits) to all methods including DDPM. We will revise the Experiments section to document the search budgets, ranges, and confirmation of identical splits. revision: yes

  2. Referee: DTE derivation: the mapping from the estimated time distribution to the final anomaly score (mode or mean) is presented as a simplification that works in practice, but the paper provides no ablation showing that alternative statistics (e.g., variance or entropy) yield materially worse detection; this choice is therefore not yet shown to be robust.

    Authors: We thank the referee for highlighting this. The selection of mode/mean is motivated by the analytical density derivation, where normal points concentrate at lower diffusion times. We will add an ablation comparing mode, mean, variance, and entropy as anomaly scores on a representative subset of ADBench datasets to empirically support the choice. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central claims rest on empirical benchmark results from ADBench comparing diffusion variants (DDPM and DTE) for anomaly detection, with DTE positioned as a practical simplification that yields an analytical density over diffusion time whose mode/mean serves as the anomaly score. No load-bearing step reduces by construction to a fitted parameter, self-citation chain, or renamed input; the derivation of the density is presented as following from the diffusion process itself, and the evaluation is external to any internal fitting loop. The work is self-contained against the stated benchmark without invoking uniqueness theorems or ansatzes from prior author work as forcing functions.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The approach rests on standard diffusion-process assumptions from DDPM literature and the empirical validity of using diffusion-time statistics as anomaly scores; no new entities are postulated.

free parameters (1)
  • neural network weights for time estimation
    Learned parameters of the deep network used to approximate the density over diffusion time.
axioms (1)
  • domain assumption The forward diffusion process follows the same Gaussian noise schedule as standard DDPM.
    Invoked when deriving the analytical form for the diffusion-time density.

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Forward citations

Cited by 2 Pith papers

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Reference graph

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