Title: Avoid Catastrophic Forgetting with Rank-1 Fisher from Diffusion Models
Primary area: transfer learning, meta learning, and lifelong learning
Keywords: continual learning, diffusion models, catastrophic forgetting, image generation, elastic weight consolidation, generative replay

Abstract: Catastrophic forgetting remains a central obstacle for continual learning in neural models.
Popular approaches---replay and elastic weight consolidation (EWC)---have limitations: replay requires a strong generator and is prone to distributional drift, while EWC implicitly assumes a shared optimum across tasks and typically uses a diagonal Fisher approximation.
In this work, we study the gradient geometry of diffusion models, which can already produce high-quality replay data.
We provide theoretical and empirical evidence that, in the low signal-to-noise ratio (SNR) regime, per-sample gradients become strongly collinear, yielding an empirical Fisher that is effectively rank-1 and aligned with the mean gradient.
Leveraging this structure, we propose a rank-1 variant of EWC that is as cheap as the diagonal approximation yet captures the dominant curvature direction.
We pair this penalty with a replay-based approach to encourage parameter sharing across tasks while mitigating drift.
On class-incremental image generation datasets (MNIST, FashionMNIST, CIFAR-10, ImageNet-1k), our method consistently improves average FID and reduces forgetting relative to replay-only and diagonal-EWC baselines. In particular, forgetting is nearly eliminated on MNIST and FashionMNIST and is roughly halved on ImageNet-1k.
These results suggest that diffusion models admit an approximately rank-1 Fisher.
With a better Fisher estimate, EWC becomes a strong complement to replay: replay encourages parameter sharing across tasks, while EWC effectively constrains replay-induced drift.

TL;DR: In diffusion, per-sample gradients become collinear in the low SNR, yielding a rank-1 Fisher. We propose a rank-1 EWC and pair it with replay. On continual learning tasks, it improves FID and nearly eliminates forgetting on MNIST and FashionMNIST.