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

cs.LGOct 8, 2026

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

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

Organizations: NVIDIA

Abstract

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.

Figures & tables

Figure 1: End-to-end pipeline of NV-Tesseract-AD.

Figure 2: Three-stage dual-axis curriculum schedule. At each stage $k$ , both the masking ratio $m_{k}$ and the diffusion timestep distribution $p_{k}(t)$ increase, implementing a monotone easy-to-hard progression over the joint difficulty space $\mathcal{D}(m,t)$ . Each stage occupies $\lfloor E/3\rfloor$ training epochs; stage boundaries are deterministic and require no hyperparameter tuning.

Hyperparameter	Value
Transformer blocks $L$	8
Hidden dimension $H$	256
Attention heads	8
FFN expansion ratio	$4\times$
Diffusion steps $N$	1,000
Variance schedule	Cosine

Table 1: Key hyperparameters of NV-Tesseract-AD.

Epoch	$S_{0}$ Avg. Loss	$S_{1}$ Avg. Loss	Loss Gap $\Delta(e)$
0	0.8511	0.8248	0.0263
30	0.1258	0.1258	0.0001
60	0.0876	0.0876	0.0001
90	0.0856	0.0855	0.0000
120	0.0894	0.0894	0.0000
150	0.0895	0.0895	0.0001

Table 2: Diffusion noise-prediction loss

\mathcal{L}_{\mathrm{diff}}

and loss gap across training epochs for complementary split-mask strategies

S_{0}

and

S_{1}

. The loss gap collapses rapidly within the first curriculum stage and remains negligible thereafter, indicating robustness to masking variation. Epoch 90 yields the lowest loss and zero gap and is selected as the evaluation checkpoint.

Figure 3: Reconstruction behavior of NV-Tesseract-AD under split-mask strategies $S_{0}$ and $S_{1}$ over the curriculum training schedule. Panel (a) shows the diffusion noise-prediction loss across epochs; loss decreases sharply in early training and stabilizes after epoch 60, with the minimum near epoch 90. Panel (b) shows the loss gap $|\mathcal{L}_{0}-\mathcal{L}_{1}|$ , which falls from 0.0263 at epoch 0 to near zero by epoch 30 and remains negligible thereafter, confirming that the curriculum produces masking-invariant reconstructions.

Metric	Baseline (2025)	NV-Tesseract-AD (2026)	Relative Change
F1	0.0376	0.1404	$\approx 3.7\times$
Precision	0.0571	0.1882	$\approx 3.3\times$
Recall	0.0280	0.1119	$\approx 4.0\times$
MAE	1.90	1.25	$\approx 34\%$ lower
MSE	3.66	1.62	$\approx 56\%$ lower

Table 3: Baseline (non-curriculum, 2025 weights) versus NV-Tesseract-AD (curriculum-trained, 2026 weights) under the same inference pipeline and evaluation set. Both models share the same Transformer diffusion backbone. MAE and MSE are computed over target entries at inference time and are distinct from the training-phase noise-prediction loss reported in § 5.1 .

Figure 4: Comparison of default unsupervised thresholding with tuned and oracle reference bounds. Bars show precision, recall, and F1 for default SCS, default MACS, the best SCS grid-search configuration, and the oracle AdjBestF1 upper bound. The oracle is an analysis-only diagnostic computed using ground-truth test labels and is not part of the deployed evaluation protocol. The gap between default unsupervised thresholding and the oracle is substantially larger than the gap between the tuned configuration and the oracle, indicating that threshold calibration remains a major bottleneck after reconstruction has been stabilized.

Figure 5: Precision, recall, and F1 as a function of percentile threshold on the residual score distribution. The best empirical trade-off appears in the 80th–90th percentile region, with peak F1 obtained near the 80th percentile. This sensitivity analysis shows that final anomaly detection quality depends strongly on calibration of the residual-score threshold even when the reconstruction model itself is stable.

Dataset Family	F1	Precision	Recall
NAB	0.9841	0.9692	1.0000
NormA	0.9477	0.9123	0.9877
NEK	0.8830	0.8261	0.9578
UCR4	0.7831	0.6872	1.0000
GutenTAG	0.6928	0.5997	0.9773
UCR	0.6409	0.5957	0.7364

Table 4: Zero-shot anomaly detection performance of NV-Tesseract-AD on EasyTSAD dataset families. The model is trained once on TSB-UAD-M and evaluated without per-dataset tuning. Point-adjusted F1 is computed using the EasyTSAD evaluation protocol [ 73 ] .

Figure 6: Precision–recall profile across EasyTSAD dataset families. Families such as NAB, NormA, and NEK lie in the high-precision/high-recall region, whereas Yahoo and WSD exhibit comparatively lower precision despite moderate-to-high recall. This pattern is consistent with the interpretation that cross-domain performance is limited more by calibration and family-specific heterogeneity than by reconstruction quality alone.

Figure 7: Trade-off between detection quality and runtime for DDPM and DPM-Solver++ variants on representative held-out datasets. The left panel shows best thresholded F1 under unsupervised calibration, while the right panel shows inference time. Faster samplers substantially reduce runtime, but also shift the operating point of the detector, demonstrating that sampling and thresholding must be validated jointly rather than treated as independent design choices.

	Oracle UB (F1)			Best Thresholded F1			Inference Time (s)
Dataset	DDPM	DPM MP	DPM S	DDPM	DPM MP	DPM S	DDPM	DPM MP	DPM S
Falling (2k)	0.1043	0.1095	0.1183	0.0690	0.0476	0.0844	562	270	99
Network Traffic	0.1818	0.1961	0.1912	0.0698	0.0964	0.0947	325	131	77
Wafer	0.1667	0.1798	0.2169	0.1089	0.0916	0.1172	380	135	94

Table 5: DDPM vs. DPM-Solver++ on representative held-out datasets. DPM MP: multi-process DPM-Solver++. DPM S: single-process DPM-Solver++. UB: oracle best-F1 using ground-truth labels for threshold selection (analysis-only diagnostic; not the deployed evaluation protocol). Inference times are dataset-level wall-clock durations; per-window latency reduction is approximately

40{\times}

(500 ms

\to

12 ms), with lower dataset-level ratios reflecting I/O and parallelism effects.

Dataset Family	Test Time (s)	Test Time (h)
UCR	339.64	0.09
UCR4	46,388.58	12.89
AIOPS	20,824.84	5.78
NAB	525.11	0.15
Yahoo	5,387.37	1.50
WSD	20,935.09	5.82

Table 6: Zero-shot EasyTSAD inference runtimes under DDPM sampling (NV-Tesseract-AD, epoch 90 checkpoint). A small number of large families dominate wall-clock cost, motivating accelerated sampling for practical benchmark evaluation.

Figure 8: Benchmark-scale inference cost across EasyTSAD dataset families under the DDPM-based evaluation protocol. A small number of large families dominate the total wall-clock cost, particularly UCR4, AIOPS, WSD, and GutenTAG. This runtime concentration highlights the practical importance of accelerated samplers for large-scale validation and deployment of diffusion-based anomaly detection systems.

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