# DeCoFlow: Structural Decomposition of Normalizing Flows for Continual Anomaly Detection

arXiv: https://arxiv.org/abs/2606.26687 · HTML: https://mlsanity.com/paper/2606.26687/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 42 references that are in the map.
- First posted on arXiv 25 Jun 2026.

## Builds on (most cited first, 30 of 33)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [Memory Aware Synapses: Learning what (not) to forget](https://mlsanity.com/paper/1711.09601/) (2017)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [Towards Total Recall in Industrial Anomaly Detection](https://mlsanity.com/paper/2106.08265/) (2021)
- [Overcoming catastrophic forgetting with hard attention to the task](https://mlsanity.com/paper/1801.01423/) (2018)
- [Training Region-based Object Detectors with Online Hard Example Mining](https://mlsanity.com/paper/1604.03540/) (2016)
- [Anomaly Detection via Reverse Distillation from One-Class Embedding](https://mlsanity.com/paper/2201.10703/) (2022)
- [SPot-the-Difference Self-Supervised Pre-training for Anomaly Detection and Segmentation](https://mlsanity.com/paper/2207.14315/) (2022)
- [CFLOW-AD: Real-Time Unsupervised Anomaly Detection with Localization via Conditional Normalizing Flows](https://mlsanity.com/paper/2107.12571/) (2021)
- [A Unified Model for Multi-class Anomaly Detection](https://mlsanity.com/paper/2206.03687/) (2022)
- [SimpleNet: A Simple Network for Image Anomaly Detection and Localization](https://mlsanity.com/paper/2303.15140/) (2023)
- [FastFlow: Unsupervised Anomaly Detection and Localization via 2D Normalizing Flows](https://mlsanity.com/paper/2111.07677/) (2021)
- [CFA: Coupled-hypersphere-based Feature Adaptation for Target-Oriented Anomaly Localization](https://mlsanity.com/paper/2206.04325/) (2022)
- [Unsupervised Continual Anomaly Detection with Contrastively-learned Prompt](https://mlsanity.com/paper/2401.01010/) (2024)
- [Hierarchical Gaussian Mixture Normalizing Flow Modeling for Unified Anomaly Detection](https://mlsanity.com/paper/2403.13349/) (2024)
- [MSFlow: Multi-Scale Flow-based Framework for Unsupervised Anomaly Detection](https://mlsanity.com/paper/2308.15300/) (2023)
- [An Incremental Unified Framework for Small Defect Inspection](https://mlsanity.com/paper/2312.08917/) (2023)
- [One-for-More: Continual Diffusion Model for Anomaly Detection](https://mlsanity.com/paper/2502.19848/) (2025)
- [MINGLE: Mixture of Null-Space Gated Low-Rank Experts for Test-Time Continual Model Merging](https://mlsanity.com/paper/2505.11883/) (2025)
- [Gated Integration of Low-Rank Adaptation for Continual Learning of Large Language Models](https://mlsanity.com/paper/2505.15424/) (2025)
- [ReplayCAD: Generative Diffusion Replay for Continual Anomaly Detection](https://mlsanity.com/paper/2505.06603/) (2025)
- [Continuous Subspace Optimization for Continual Learning](https://mlsanity.com/paper/2505.11816/) (2025)
- [AnaCP: Toward Upper-Bound Continual Learning via Analytic Contrastive Projection](https://mlsanity.com/paper/2511.13880/) (2025)
- [VQ-Flow: Taming Normalizing Flows for Multi-Class Anomaly Detection via Hierarchical Vector Quantization](https://mlsanity.com/paper/2409.00942/) (2024)

## Abstract (arXiv)

In industrial environments, new product categories arrive sequentially, requiring continual anomaly detection without access to past data. Normalizing Flows (NFs) provide exact density estimation but suffer from catastrophic forgetting as parameter updates across tasks distort the density manifold. While parameter isolation can prevent interference, it must preserve the strict invertibility and Jacobian validity of NFs. To satisfy these requirements, we exploit the inherent property that affine coupling layers maintain transformation validity regardless of subnet parameterization. Based on this, we propose DeCoFlow, which decomposes subnets into a frozen universal base and task-specific low-rank adapters to isolate updates. We further introduce Task-Specific Alignment, Auxiliary Coupling Layers, and Tail-Aware Loss to compensate for frozen-base rigidity. DeCoFlow achieves state-of-the-art image-level AUROCs of 98.40% on MVTec-AD and 93.00% on VisA, while maintaining parameter-level zero forgetting (0.00% FM under correct routing) with only 2.27M parameters per task.