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Continual Unsupervised Generative Modelling via Online Optimal Transport
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Proposes SDDM, a dual dynamic memory with Sinkhorn optimal-transport-based sample selection and dynamic model expansion for unsupervised continual generative modelling (DDPM) under task-free online settings, also tested on supervised continual classification.
Problem
Continual generative modelling without task or class labels at training or inference, where catastrophic forgetting degrades image generation quality and standard memory methods rely on supervised signals.
Approach
A temporary FIFO memory plus a dynamic expansion memory whose representative samples are added only when Sinkhorn distance to all existing representatives exceeds a threshold; memory blocks are allocated by Sinkhorn distance, and the DDPM is expanded with new noise-estimator experts when expert distributions diverge.
Key results
- On class-incremental unsupervised generation, SDDM-Dyn reaches an average FID of 46.49 (vs 51.44 for SDDM and 55.21 for CVA-style baseline, with CGKD-VAE at 56.39 and CGKD-GAN at 84.72 in the average column of Table 1).
- On supervised continual classification, SDDM reaches 74.63% on Split CIFAR10 vs 74.42% for DER+++refresh and 72.70% for DER++.
- On Split TinyImageNet, SDDM reaches 21.36% vs 20.81% for DER+++refresh; on P-MNIST 90.39% vs 88.21% for DER++.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use dynamic model expansion (SDDM-Dyn) instead of SDDM | SDDM · Split MNIST | FID: 23.36 -> 18.48 | Helped |
| use dynamic model expansion (SDDM-Dyn) instead of SDDM | SDDM · Split Fashion | FID: 47.43 -> 42.76 | Helped |
| use dynamic model expansion (SDDM-Dyn) instead of SDDM | SDDM · Split SVHN | FID: 55.16 -> 51.21 | Helped |
| use dynamic model expansion (SDDM-Dyn) instead of SDDM | SDDM · Split CIFAR10 | FID: 79.83 -> 73.52 | Helped |
| use SDDM memory instead of DER+++refresh | continual classification · Split CIFAR10 | accuracy: 74.42 ± 0.82 -> 74.63 ± 1.32 | Helped |
| use SDDM memory instead of DER+++refresh | continual classification · Split TI | accuracy: 20.81 ± 1.28 -> 21.36 ± 1.17 | Helped |
| use SDDM memory instead of DER++ | continual classification · P-MNIST | accuracy: 88.21 ± 0.39 -> 90.39 ± 0.41 | Helped |
| vary the Sinkhorn memory-expansion threshold λ (ablation) | SDDM · Split MNIST | FID | No clear effect |
| set λ = 46 for memory-block expansion (ablation) | SDDM · Split MNIST | memory cluster formation | Helped |
Surprising findings
- The proposed SDDM still achieves good generation performance even when it creates no additional memory blocks (per the ablation on lambda).
- Table 1 has a column labelled CVA whose results appear to be the SDDM-Dyn variant, making the table's labelling ambiguous.
Limitations
- The expansion thresholds lambda and lambda_d are tuned experimentally per dataset rather than set automatically.
- Evaluation is limited to small-resolution image datasets for class-incremental streams, with high-resolution results only on a few datasets.
- Theoretical bound relies on assumptions (probabilistic Lipschitzness) that are not verified empirically.
Experimental setup
Datasets: MNIST Fashion-MNIST SVHN CIFAR10 CelebA-HQ CACD FFHQ Split TinyImageNet Permuted MNIST
Benchmarks: Split MNIST Split Fashion Split SVHN Split CIFAR10 CelebA-HQ CACD FFHQ Split CIFAR10 (classification) Split TinyImageNet P-MNIST
Metrics: FID average classification accuracy
Baselines: R-VAE R-DDPM CGKD-GAN CGKD-DDPM CGKD-WAE CGKD-VAE GSS DER DER++ DER+++refresh
Builds on: DDPM Sinkhorn distance DER++ Online task-free continual learning (MIR/gradient-based memory)
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