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A Geometric Framework for Understanding Memorization in Generative Models
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Proposes the manifold memorization hypothesis, framing memorization as a model manifold having too low local intrinsic dimension relative to the data manifold, and validates it on synthetic data, CIFAR10 and Stable Diffusion with LID-based detection and token-level mitigation.
Problem
Memorization in deep generative models lacks a unifying theoretical explanation; existing formal definitions are probability-mass based and intractable at scale, and provide little explanatory power for observed memorization phenomena.
Approach
Memorization occurs at a point when the learned model manifold contains it but has too small local intrinsic dimension there relative to the ground truth; this splits memorization into overfitting-driven (LID_theta < LID_*) and data-driven (low LID_* ground truth) types, enabling LID-based detection and CFG-token-attribution mitigation.
Key results
- On CIFAR10, estimated LID_theta is generally smaller for memorized than non-memorized generated images for both iDDPM and StyleGAN2-ADA.
- On Stable Diffusion v1.5, all LID_theta proxies (unconditional, conditional, CFG vector norm) assign smaller values to 86 memorized LAION images than to non-memorized images; CFG norm gives the strongest signal.
- Token-level mitigation guided by the FLIPD-based attribution lowers SSCD similarity as k increases while keeping CLIP score higher than uniform random token selection, though it performs on par with the CFG-based variant rather than better.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use estimated model LID to distinguish memorized from non-memorized samples | iDDPM and StyleGAN2-ADA · CIFAR10 | LID of generated samples | Helped |
| Use conditional or unconditional LID, or CFG vector norm, as a memorization signal | Stable Diffusion v1.5 · LAION memorized and non-memorized images | memorization detection | Helped |
| Use unconditional LID instead of requiring caption information | Stable Diffusion v1.5 · LAION memorized and non-memorized images | memorization detection | Helped |
| Normalize LID estimates by PNG compression length | CIFAR10 and Stable Diffusion memorization detection · CIFAR10 and Stable Diffusion | separation of memorized and non-memorized images | Helped |
| Use token attributions to choose prompt tokens to perturb | Stable Diffusion sample-time mitigation · Matching prompts | SSCD similarity | Helped |
| Use token attributions to choose prompt tokens to perturb | Stable Diffusion sample-time mitigation · Matching prompts | CLIP score | Helped |
| Replace the CFG-vector-norm attribution metric with FLIPD (ablation) | Stable Diffusion sample-time mitigation · Matching prompts | memorization mitigation performance | No clear effect |
| Select tokens uniformly instead of using memorization-metric attributions (ablation) | Stable Diffusion sample-time mitigation · Matching prompts | SSCD similarity | Hurt |
| Select tokens uniformly instead of using memorization-metric attributions (ablation) | Stable Diffusion sample-time mitigation · Matching prompts | CLIP score | Hurt |
| Increase the number of perturbed prompt tokens k (ablation) | Stable Diffusion sample-time mitigation · Matching prompts | SSCD similarity | Helped |
| Increase the number of perturbed prompt tokens k (ablation) | Stable Diffusion sample-time mitigation · Matching prompts | CLIP score | Hurt |
Surprising findings
- Optimizing the prompt to maximize FLIPD-based LID at sample time can produce chaotic textures with artificially high LID estimates, so direct optimization fails.
- Data-driven memorization cannot be detected by comparing training and test likelihoods, and the (lambda, gamma)-copy definition misses it entirely.
Limitations
- LID_theta estimates overlap between memorized and non-memorized samples, and image simplicity confounds the signal.
- No LID_* estimator scales to Stable Diffusion, so overfitting vs data-driven memorization cannot be separated at that scale.
- The FLIPD-based mitigation performs on par with, but does not outperform, the CFG-norm mitigation.
Experimental setup
Datasets: CIFAR10 LAION COCO Tuxemon LAION Aesthetics 6.5+
Benchmarks: CIFAR10 memorization labels LAION memorized images (86 matching verbatim)
Metrics: LID estimate distributions CLIP score SSCD similarity
Baselines: SSCD distance calibrated l2 distance CFG vector norm uniform random token selection
Builds on: manifold hypothesis FLIPD normal bundle LID estimator Gaussian-based memorization definition (lambda, gamma)-copy differentiable memorization metric of Chen et al. (token attribution)
Closest papers by meaning
- On the Edge of Memorization in Diffusion Models (NeurIPS 2025 · similarity 0.88)
- Towards Memorization Estimation: Fast, Formal and Free (ICML 2025 · similarity 0.87)
- Understanding and Mitigating Memorization in Generative Models via Sharpness of Probability Landscapes (ICML 2025 · similarity 0.87)
- What Secrets Do Your Manifolds Hold? Understanding the Local Geometry of Generative Models (ICLR 2025 · similarity 0.87)
- Memorization Through the Lens of Curvature of Loss Function Around Samples (ICML 2024 · similarity 0.87)
- Why Diffusion Models Don’t Memorize: The Role of Implicit Dynamical Regularization in Training (NeurIPS 2025 · similarity 0.87)
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