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NV-Tesseract-AD: Curriculum-Enhanced Conditional Diffusion for Multivariate Time-Series Anomaly Detection

Aditi Gautam, Manikandan Ravikiran, Saira Qureshi, Sena Fatma Ekiz, Charan Jagwani, Mahmoud Elhadidy, Sanjeev Roka

arXiv:2610.12754v1cs.LG

TL;DR

Multivariate time-series anomaly detection must handle complex streams where anomaly labels may be sparse, while diffusion training can expose models to uneven reconstruction difficulty. NV-Tesseract-AD combines conditional diffusion with a staged curriculum over masking and noise, reporting masking-invariant reconstruction and improved detection relative to a non-curriculum baseline.

  • Problem

    Multivariate time-series anomaly detection faces high-dimensional, non-stationary streams and sparse or unavailable anomaly labels, while uniform diffusion training exposes models to the full difficulty spectrum from initialization.

    Source: §1 · p. 1, §3.5 · p. 13

  • Method

    NV-Tesseract-AD uses a Transformer-based conditional diffusion model with a three-stage easy-to-hard curriculum over masking severity and diffusion noise.

    Source: §1 · pp. 2–3

  • Results

    The dual-axis curriculum yields masking-invariant reconstruction and ≈3.7× improvement in F1 relative to a non-curriculum baseline.

    Source: §1 · p. 3

  • Takeaways & Limitations

    The results support reconstruction-centric diffusion training as a practical and generalizable design principle for multivariate anomaly detection.

    Source: §6 · p. 32

    Unsupervised threshold calibration is the dominant remaining detection bottleneck; reconstruction quality is not the limiting factor.

    Source: §5.7 · p. 31

Abstract

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We propose NV-Tesseract-AD, a curriculum learning-enhanced conditional diffusion framework for multivariate time-series anomaly detection. Our central hypothesis is that reconstruction difficulty can be explicitly structured along two complementary axes, masking severity and diffusion noise level, and that training from easier to harder tasks along both axes simultaneously stabilizes optimization and improves residual discriminability. We integrate a Transformer-based diffusion backbone with a three-stage dual curriculum over masking ratios and diffusion timesteps, retaining anomalous samples throughout training and relying on structured corruption to drive self-supervised representation learning. We evaluate NV-Tesseract-AD under two regimes: in-distribution training on the TSB-UAD-M corpus and strict zero-shot transfer to ten EasyTSAD benchmark families without per-dataset tuning. The dual-axis curriculum produces masking-invariant reconstruction, confirmed by a near-zero loss gap between complementary masking strategies within the first training stage, and yields an approximately 3.7-fold improvement in F1 and a 56 percent reduction in MSE relative to a non-curriculum baseline. Zero-shot performance reaches F1 = 0.984 on NAB and F1 = 0.948 on NormA. Weaker results on heterogeneous families are traced to unsupervised threshold calibration rather than reconstruction quality, identifying calibration as the dominant remaining detection bottleneck. Accelerated inference via DPM-Solver++ reduces sampling cost by a factor of 3.5 to 5.7 at the dataset level but couples to thresholding behavior, establishing that the sampler and threshold must be validated jointly. Together, these findings demonstrate that aligning diffusion denoising difficulty with curriculum learning principles provides a principled and practical approach for robust anomaly detection in complex multivariate time series.

1 Introduction

Multivariate time-series anomaly detection must contend with high-dimensional, non-stationary streams, missing observations, and sparse labels. NV-Tesseract-AD organizes reconstruction difficulty across masking and diffusion noise, reporting improved reconstruction and detection results, including in zero-shot transfer.

1 Introduction

  • The task matters across manufacturing, energy, and finance, but real-world streams may be high-dimensional, non-stationary, structurally incomplete, and sparsely labeled.The objective is to identify timestamps or windows whose dynamics deviate from learned normal patterns.Source: §1 · pp. 1–2
  • Uniform diffusion training exposes the model to heterogeneous denoising difficulty from initialization, while masking further increases reconstruction difficulty as more observed values are withheld.The paper identifies joint management of these difficulties in multivariate time-series diffusion anomaly detection as underexplored.Source: §1 · p. 2
  • The framework retains anomalous samples and uses structured corruption for self-supervised conditional imputation rather than filtering anomalies from training data.Evaluation covers TSB-UAD-M and strict zero-shot transfer to ten EasyTSAD dataset families without per-dataset tuning.Source: §1 · p. 2
  • ≈3.7× improvement in F1 and 56% reduction in MSE relative to a non-curriculum baseline accompany masking-invariant reconstruction.The complementary-mask loss gap is near zero by the end of the first training stage; zero-shot F1 reaches 0.984 on NAB and 0.948 on NormA.Source: §1 · p. 3
  • The contributions combine a dual-axis curriculum, masking-invariant generalization, and a threshold-calibration analysis of the remaining detection bottleneck.The paper reports improved reconstruction fidelity and detection performance across benchmark families under a strict zero-shot protocol.Source: §1 · p. 3
  • NV-Tesseract-AD uses a Transformer-based conditional diffusion architecture with a three-stage curriculum over masking severity and diffusion noise level.The schedule progresses from easier to harder tasks along both axes.Source: §1 · pp. 2–3

2 Related Work

Related work spans time-series anomaly detection, generative and diffusion models, and curriculum learning, but the paper identifies a gap in jointly scheduling masking and noise difficulty for diffusion-based multivariate anomaly detection. It also motivates systematic analysis of threshold calibration’s contribution to the reconstruction–detection gap.

2.1 Time Series Anomaly Detection

  • Prior time-series anomaly detectors range from statistical and recurrent methods to Transformers, while generative diffusion methods use reconstruction or likelihood signals but commonly train with uniform schedules.The review notes that existing systems can face non-stationarity, weak supervision, training instability, or train–test mismatch.Source: §2.1 · p. 3

2.2 Generative Models for Anomaly Detection

  • Generative anomaly detection includes GANs, VAEs, and diffusion systems, with diffusion variants combining conditional generation, decomposition, graph encoders, and latent representations.The reviewed diffusion systems generally retain fixed corruption processes or uniform timestep sampling, leaving denoising difficulty unmanaged.Source: §2.2 · p. 4

2.3 Diffusion Models for Time Series

  • Time-series diffusion supports forecasting, imputation, and anomaly detection using sequence-aware backbones, while many anomaly-detection models still use uniform timestep sampling and fixed corruption.The review also describes adaptive noise schedules and importance-weighted timestep sampling for diffusion models.Source: §2.3 · pp. 4–5

2.4 Curriculum Learning in Time Series

  • Time-series curricula have varied prediction horizons, data volatility, window lengths, and training subsets, with reviewed studies reporting benefits from progressing toward harder data.One reviewed anomaly-detection study found model-complexity curricula alone did not help unless combined with data curricula.Source: §2.4 · p. 5

2.5 Curriculum Schedules in Diffusion Models

  • Diffusion curricula have scheduled noise levels, timesteps, or other corruption axes, but the reviewed approaches do not jointly address masking severity and diffusion noise for this anomaly-detection setting.The paper frames high masking combined with high noise as harder than either axis alone and motivates a joint difficulty measure.Source: §2.5 · pp. 5–6, §2.6 · p. 6

2.6 Gap and Motivation

  • The paper identifies three gaps: no unified diffusion–Transformer–curriculum framework for multivariate time-series anomaly detection, no systematic joint scheduling of masking and noise, and limited analysis of threshold calibration’s role.It proposes a dual-axis conditional diffusion framework and evaluates it under a strict zero-shot protocol while decomposing the reconstruction–detection gap.Source: §2.6 · pp. 6–7

3.1 Method Overview

NV-Tesseract-AD treats masked conditional reconstruction as a diffusion-denoising task and stages training from easier to harder conditions across masking and noise. A Transformer denoiser supports this curriculum, and reconstructed values feed residual-based anomaly scoring.

3.1 Method Overview

  • The conditional diffusion process corrupts only withheld target entries, preserving conditioning entries as clean contextual anchors for denoising.The reverse process is parameterized by a learned denoising network.Source: §3.1 · p. 7
  • A residual Transformer denoiser uses corrupted targets, clean context, mask indicators, timestep embeddings, and curriculum-stage embeddings.Gated residual connections are used to stabilize learning under high-noise inputs.Source: §3.1 · p. 7
  • Training difficulty increases across three stages by expanding both the masking ratio and the sampled diffusion-timestep range.The schedule follows a monotone progression over a joint difficulty measure.Source: §3.1 · p. 7
  • At inference, the denoiser reconstructs held-out entries and normalized reconstruction residuals provide pointwise anomaly scores that are thresholded into binary decisions.Figure 1 is described as tracing the pipeline from a training window through curriculum-controlled corruption and denoising to anomaly scoring.Source: §3.1 · p. 9

3.2 Problem Setup

The setup represents each multivariate window with an observation mask that distinguishes available entries from structural missingness. Training partitions available entries into conditioning context and withheld targets for self-supervised conditional imputation.

3.2 Problem Setup

  • Structural missing entries are excluded from both diffusion loss and downstream anomaly scoring, so sensor dropout is not treated as an anomaly indicator.The observation mask marks available entries as 1 and structurally missing entries as 0.Source: §3.2 · p. 9
  • Each training window splits observed entries into disjoint conditioning and target subsets, with the target subset withheld for supervision.The masking ratio is the fraction of observed entries withheld per window.Source: §3.2 · p. 9
  • The model learns to infer withheld observations from partial context without anomaly labels, using a denoising objective that predicts added Gaussian noise on target entries.The reverse process implicitly samples conditional clean targets, which are compared with observed values for anomaly detection.Source: §3.2 · p. 9

3.3 Masked Conditional Diffusion Reconstruction

The model corrupts only withheld target entries while preserving clean conditioning context and excluding structurally missing values. It predicts the added noise and uses that prediction to recover clean estimates for target supervision and anomaly scoring.

3.3.1 Forward Diffusion Process

  • A cosine-schedule DDPM corrupts target entries while leaving conditioning values clean, preserving the context needed for conditional denoising.The cosine schedule preserves higher signal fidelity at low timesteps, which the paper found beneficial for retaining fine temporal structure during easy curriculum stages.Source: §3.3.1 · p. 10, §3.3.2 · p. 10

3.3.2 Masked Conditional Corruption

  • Masked conditional corruption keeps observed context intact, corrupts withheld observed targets according to the timestep, and excludes structurally missing entries from inputs and loss.This mirrors inference-time imputation, where observed variables anchor reconstruction of others.Source: §3.3.2 · p. 10

3.3.3 Reverse Denoising and Clean Signal Recovery

  • The denoiser predicts Gaussian noise, which is reparameterized into a clean estimate; only target estimates are supervised and scored while conditioning entries remain fixed.At inference, iterative reverse denoising starts from sampled noise at target positions and produces a reconstruction from the learned conditional distribution.Source: §3.3.3 · p. 11

3.4 Transformer-Based Diffusion Denoiser

A Transformer denoiser represents each time step using series values, temporal and diffusion-step information, masks, and curriculum stage. Full temporal self-attention and gated residual refinement support reconstruction across noise levels.

3.4.1 Input Representation and Token Construction

  • Each time-step token combines corrupted or clean series values with diffusion-step, temporal-position, mask, and curriculum-stage information.The stage embedding lets the model distinguish denoising regimes, with stage 3 supplied at test time for its most general denoising policy.Source: §3.4.1 · p. 11

3.4.2 Residual Transformer Backbone

  • The residual Transformer applies full self-attention across time steps, using future context, while concatenating channels lets shared representations model cross-variable interactions without quadratic cost in D.This design accommodates training files ranging from 2 to 64 channels after preprocessing.Source: §3.4.2 · p. 12

3.4.3 Gated Residual Refinement

  • A learned gate adaptively filters each block’s update, suppressing noisy updates at high noise and permitting stronger feature refinement at low noise.The gate complements the curriculum by adjusting update magnitude to sample-level difficulty within a stage.Source: §3.4.3 · pp. 12–13

3.5 Dual-Axis Curriculum Learning

NV-Tesseract-AD organizes reconstruction difficulty jointly by masking severity and diffusion noise, then trains through three increasingly difficult stages. The progression is intended to stabilize early optimization and support residual separability.

3.5 Dual-Axis Curriculum Learning

  • Standard diffusion training combines fixed masking with uniform timestep sampling, exposing an untrained model immediately to high-masking, high-noise tasks.The paper argues this contributes to slow convergence and large residual variance in standard diffusion-based anomaly detectors.Source: §3.5 · p. 13

3.5.1 Formal Difficulty Measure

  • D(m, t) combines masking ratio m and inverse signal-to-noise ratio multiplicatively, increasing with both masking and timestep to represent their compounded reconstruction difficulty.The measure justifies ordering configurations; it is not an explicit optimization objective.Source: §3.5.1 · pp. 13–14

3.5.2 Stage-Wise Curriculum Schedule

  • The three-stage dual-axis curriculum monotonically increases masking ratio and diffusion timestep distribution from easy to hard; each stage occupies floor(E/3) training epochs, with deterministic boundaries requiring no tuning.Stage 1 withholds 10% of observed entries and samples timesteps uniformly from 1–333; stage 3 withholds 50%.Source: Figure 2 · p. 14, §3.5.2 · p. 14

3.5.3 Optimization Intuition and Theoretical Motivation

  • The proposed rationale is that easier early tasks establish stable temporal and cross-variable representations before harder stages, while low-variance normal reconstructions can improve anomalous-versus-normal residual separability.The curriculum is described as progressively expanding the reconstruction manifold from a well-conditioned subproblem to the full difficulty range.Source: §3.5.3 · p. 15

3.6 Training Objective

Training combines masked noise prediction with temporal derivative consistency terms. The derivative losses regularize reconstructions toward continuity and smoothness while respecting which entries are observed.

3.6.1 Primary Diffusion Loss

  • The primary diffusion loss predicts Gaussian noise only on withheld observed target entries, with timestep sampling determined by the curriculum stage.Conditioning entries and structurally missing entries do not contribute to the gradient signal.Source: §3.6.1 · p. 15

3.6.2 Velocity Consistency Regularization

  • Velocity consistency penalizes mismatches between predicted and true first-order temporal differences only where consecutive entries are observed.The L1 penalty is more robust to occasional large-derivative patterns such as industrial step changes.Source: §3.6.2 · p. 16

3.6.3 Acceleration Consistency Regularization

  • Acceleration consistency penalizes second-order differences over three consecutive observed entries, encouraging smoother reconstructions for smooth-process time series.Together with velocity consistency, it encourages reconstructions on a smoother manifold than noise prediction alone.Source: §3.6.3 · p. 16

3.6.4 Final Combined Loss and Weighting

  • The combined objective adds velocity and acceleration consistency losses to diffusion loss, weighted at 0.1 and 0.05 so derivative regularization remains non-dominant.The smaller acceleration weight reflects the stated preference for first-order continuity over second-order smoothness in the benchmark’s industrial time series.Source: §3.6.4 · p. 17

3.7 Inference and Anomaly Scoring

Inference reconstructs masked observations through reverse diffusion, then converts reconstruction residuals into pointwise and window-level anomaly scores. Sampling uses an accelerated solver, while validation data sets the decision threshold.

3.7.1 Stochastic Reconstruction via Reverse Diffusion

  • Each test window is reconstructed through reverse diffusion using complementary masks that split observed entries between conditioning and targets.The deterministic alternating split gives full observed-signal coverage over two reconstruction passes if needed.Source: §3.7.1 · p. 17
  • DPM-Solver++ uses 25 reverse steps and reduces per-window inference time by approximately 40× versus DDPM’s 1,000 steps.The reported latency falls from approximately 500 ms to 12 ms per window.Source: §3.7.1 · p. 17

3.7.2 Pointwise Anomaly Score Computation

  • The pointwise score is the normalized mean absolute reconstruction residual over observed channels at each timestamp.Normalization prevents timestamps with fewer observed channels from receiving systematically lower scores because of structural missingness.Source: §3.7.2 · p. 18

3.7.3 Window-Level Score and Threshold Decision

  • Window-level scores summarize pointwise scores, while timestamp-level detection uses pointwise scores thresholded at a validation-selected value.The threshold is chosen on held-out validation data by maximizing F1.Source: §3.7.3 · p. 18

4 Experimental Setup

The experimental setup evaluates NV-Tesseract-AD on a heterogeneous multivariate training corpus and held-out cross-domain benchmarks, including zero-shot EasyTSAD families. It specifies the preprocessing, metrics, and implementation used for those evaluations.

4 Experimental Setup

  • Evaluation covers heterogeneous-corpus training and zero-shot transfer to held-out benchmark families without per-dataset fine-tuning.The setup describes datasets, evaluation metrics, and implementation details for both regimes.Source: §4 · p. 18

4.1 Datasets

  • TSB-UAD-M combines multivariate series from the TSB-AD suite, spanning 2–248 channels and multiple application domains.The corpus derives from 1,070 labeled series overall, including 200 multivariate series; preprocessing standardizes dimensionality to 64 and uses a stratified 70/30 split.Source: §4.1 · pp. 18–19
  • Cross-domain evaluation uses five held-out datasets, alongside EasyTSAD’s ten families with distinct anomaly semantics and labeling conventions.The five datasets are Wafer Manufacturing, CalIt2 Building People Counts, Network Traffic, Genesis Demonstrator, and Falling People.Source: §4.1 · p. 19

4.2 Evaluation Metrics

  • Point-adjusted F1 is the primary detection metric, with thresholds selected by validation F1 and no test-data calibration.The score is the normalized mean absolute residual over observed channels; AUROC is omitted because EasyTSAD lacks a standard variant across its ten families.Source: §4.2 · pp. 19–20
  • Masked MAE and MSE assess reconstruction fidelity over target entries, while diffusion noise-prediction loss tracks training stability.These reconstruction measures characterize improvement independently of thresholding; the training loss tracks stability under complementary masking strategies.Source: §4.2 · pp. 19–20

4.3 Implementation Details

  • Inference uses DPM-Solver++ with 25 reverse steps and eight samples aggregated by the elementwise median.Per-window latency falls from approximately 500 ms to 12 ms, while dataset-level runtime reductions are 3.5–5.7×; inference fixes the curriculum stage at k = 3.Source: §4.3 · p. 20
  • The denoiser is an eight-block residual Transformer with 256 hidden dimensions and eight-head self-attention.Training uses 100 epochs across three equal stages, increasing masking ratios from 0.1 to 0.5 while sampling diffusion timesteps from successive thirds of the schedule.Source: §4.3 · p. 21
  • Evaluation windows use stride 1 for fine-grained localization, and training uses stride 10 to balance data diversity and computational cost.Training uses AdamW with a cosine learning-rate schedule, warmup, gradient clipping, and validation-F1-based early stopping; full training takes approximately 18 hours on one A100 GPU.Source: §4.3 · pp. 21–22

5 Results and Discussion

The results assess reconstruction stability, downstream detection, zero-shot transfer, calibration, and runtime. They report gains over a non-curriculum baseline while identifying threshold calibration and sampler–threshold interaction as practical concerns.

5.1 Reconstruction Stability Under Complementary Masking

  • The loss gap between complementary masking strategies falls from 0.0263 at initialization to approximately zero by epoch 30 and remains negligible thereafter.The loss stabilizes after about epoch 60 and reaches its minimum near epoch 90; mild deterioration at epochs 120–160 is attributed to possible overfitting to the hardest curriculum stage.Source: §5.1 · pp. 22–23, Table 2 · p. 23, Figure 3 · p. 23

5.2 Effect of Curriculum Training and Train–Inference Alignment

  • ≈3.7× improvement in F1 and 56% reduction in MSE are reported for NV-Tesseract-AD versus the non-curriculum baseline.Both models use the same Transformer diffusion backbone; the comparison uses a common evaluation pipeline.Source: Table 3 · p. 24, §5.2 · p. 24

5.3 From Reconstruction Residuals to Anomaly Decisions

  • Default unsupervised thresholding is the dominant remaining detection bottleneck after reconstruction stabilizes.The default-to-oracle gap is substantially larger than the tuned-grid-search-to-oracle gap; the best empirical F1 trade-off lies around the 80th–90th percentile of residual scores.Source: Figure 4 · p. 25, §5.3 · pp. 25–26, Figure 5 · p. 26

5.4 Zero-Shot Transfer Across EasyTSAD Families

  • Zero-shot F1 ranges from 0.9841 on NAB and 0.9477 on NormA to 0.4328 on Yahoo and 0.3406 on WSD.The model is trained once on TSB-UAD-M and evaluated across EasyTSAD families without dataset-specific tuning; the paper relates weaker-family results to threshold calibration and heterogeneity.Source: §5.4 · pp. 26, 28, Table 4 · p. 27, Figure 6 · p. 27

5.5 Fast Samplers Improve Feasibility but Shift Operating Points

  • DPM-Solver++ reduces dataset-level inference time by approximately 3.5–5.7×, while its effect on thresholded F1 varies across datasets and variants.Different reverse-step counts shift residual-score distributions, so the sampler and thresholding behavior require joint validation.Source: §5.5 · pp. 28–29, Table 5 · p. 28, Figure 7 · p. 29

5.6 Benchmark-Scale Runtime and Practical Implications

  • Full-suite EasyTSAD evaluation under DDPM takes 112,504.59 seconds, with UCR4, WSD, AIOPS, and GutenTAG accounting for over 90% of runtime.The paper reports that DPM-Solver++ reduces dataset-level suite runtime by 3.5–5.7×.Source: §5.6 · pp. 29, 31, Table 6 · p. 30, Figure 8 · p. 30

5.7 Overall Interpretation

  • The paper concludes that practical zero-shot detection depends on stable reconstruction, calibrated thresholding, and efficient sampling being designed and validated together.Its overall interpretation identifies threshold calibration as the dominant remaining detection bottleneck and says sampler choice changes thresholding behavior.Source: §5.7 · p. 31

6 Conclusions and Future Work

NV-Tesseract-AD structures reconstruction difficulty along masking and diffusion-noise axes, and experiments support this hypothesis. Zero-shot transfer is competitive, while threshold calibration and inference cost remain deployment bottlenecks.

6 Conclusions and Future Work

  • The split-mask diffusion noise-prediction loss gap falls from 0.0263 at initialization to effectively zero within the first curriculum stage and remains negligible.The authors interpret this as masking-invariant generalization without explicit invariance constraints.Source: §6 · p. 32
  • ≈3.7× improvement in F1 and 56% reduction in MSE versus a non-curriculum baseline accompany curriculum training with consistent train–inference preprocessing.Small mismatches in normalization, masking, inference schedule, or stage embeddings can dominate end-to-end detection performance.Source: §6 · p. 32
  • F1 = 0.9841 on NAB and F1 = 0.9477 on NormA under strict zero-shot evaluation across EasyTSAD families without per-dataset tuning.The protocol trains once on TSB-UAD-M.Source: §6 · p. 32
  • Unsupervised threshold calibration accounts for most of the model-capability-to-deployed-performance gap, while DPM-Solver++ yields 3.5–5.7× dataset-level speedups but couples to thresholding.The authors identify calibration-free thresholding as an open problem and say sampler and threshold must be validated jointly.Source: §6 · p. 32
  • Future directions include inferring stable score geometry without labels and using detection-centric objectives to widen normal–anomalous residual gaps.The authors also propose reducing reliance on post-hoc thresholding.Source: §6 · p. 32
  • A theoretical account of why staged masking and noise schedules stabilize diffusion optimization remains an open question.Source: §6 · p. 33
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