Distributional Statistics Restore Training Data Auditability in One-step Distilled Diffusion Models

Muxing Li; Zesheng Ye; Sharon Li; Andy Song; Guangquan Zhang; Feng Liu

Home/Archive/arXiv

arXiv · 2502.02970

Distributional Statistics Restore Training Data Auditability in One-step Distilled Diffusion Models

Muxing Li·Zesheng Ye·Sharon Li·Andy Song·Guangquan Zhang·Feng Liu

View original source ↗Read source document ↗Export metadata ↓

Abstract

The proliferation of diffusion models trained on web-scale, provenance-uncertain image collections has made it essential, yet technically unresolved, to determine whether a model has learned from specific copyrighted data without authorization. Current methods primarily rely on the memorization effect, whereby models reconstruct their training images better than unseen ones, to detect unauthorized training data on a per-instance basis. This effect, however, vanishes under distillation, the now-dominant deployment pipeline that compresses compute-intensive teacher diffusion models into efficient {\em student one-step generators} mimicking the teacher's output for real-time user access. As the students train exclusively on teacher-generated outputs and never directly see the teacher's original training data, they carry no per-instance memorization of that upstream data, creating a model laundering loophole that severs the auditable link between a deployed model and its upstream training data. We nonetheless reveal that a distributional memory chain survives under distillation: the student's output distribution remains closer to the teacher's training distribution than to any non-training reference, even if no single training instance is memorized. Exploiting this chain, we develop a distributional unauthorized training data detector, grounded in kernel-based distribution discrepancy, that determines if a candidate dataset of unknown composition is statistically aligned with the student-generated distribution more than held-out non-training datasets, thus tracing provenance back to the teacher's training data. Evaluation across benchmarks and distillation setups confirms reliable detection even when unauthorized data forms a minority of the candidate set, establishing distribution-level auditing as a countermeasure to model laundering and a paradigm for accountable generative AI ecosystems.

Explore related subjects

cs.LG

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Muxing Li, Zesheng Ye, Sharon Li, Andy Song, Guangquan Zhang, Feng Liu. 2026-04-02. Distributional Statistics Restore Training Data Auditability in One-step Distilled Diffusion Models. https://arxiv.org/abs/2502.02970

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Random Polytope Descriptors

We introduce a class of random polytopes which simultaneously generalizes several known constructions. While being fairly general, these polytopes are also computationally exceptionally benign. We indicate how these properties can be exploited for classification and clustering tasks in data analysis. Crucially, our construction lets users smoothly trade off between a tighter description of the data and faster computation.

cs.LG↗

arXiv2026

CurvFed: Curvature-Aligned Federated Learning for Fairness without Demographics

Modern human sensing applications often rely on data distributed across users and devices, where privacy concerns prevent centralized training. Federated Learning (FL) addresses this challenge by enabling collaborative model training without exposing raw data or attributes. However, achieving fairness in such settings remains difficult, as most human sensing datasets lack demographic labels, and FL's privacy guarantees limit the use of sensitive attributes. This paper introduces CurvFed: Curvature Aligned Federated Learning for Fairness without Demographics, a theoretically grounded framework that promotes fairness in FL without requiring any demographic or sensitive attribute information, a concept termed Fairness without Demographics (FWD), by optimizing the underlying loss landscape curvature. Building on the theory that equivalent loss landscape curvature corresponds to consistent model efficacy across sensitive attribute groups, CurvFed regularizes the top eigenvalue of the Fisher Information Matrix (FIM) as an efficient proxy for loss landscape curvature, both within and across clients. This alignment promotes uniform model behavior across diverse bias inducing factors, offering an attribute agnostic route to algorithmic fairness. CurvFed is especially suitable for real world human sensing FL scenarios involving single or multi user edge devices with unknown or multiple bias factors. We validated CurvFed through theoretical and empirical justifications, as well as comprehensive evaluations using three real world datasets and a deployment on a heterogeneous testbed of resource constrained devices. Additionally, we conduct sensitivity analyses on local training data volume, client sampling, communication overhead, resource costs, and runtime performance to demonstrate its feasibility for practical FL edge device deployment.

cs.LG↗

arXiv2026

Path Regularization: A Near-Complete and Optimal Nonasymptotic Generalization Theory for Multilayer Neural Networks and Double Descent Phenomenon

Path regularization has shown to be a very effective regularization to train neural networks, leading to a better generalization property than common regularizations i.e. weight decay, etc. We propose a first near-complete (as will be made explicit in the main text) nonasymptotic generalization theory for multilayer neural networks with path regularizations for general learning problems. In particular, it does not require the boundedness of the loss function, as is commonly assumed in the literature. Our theory goes beyond the bias-variance tradeoff and aligns with phenomena typically encountered in deep learning. It is therefore sharply different from other existing nonasymptotic generalization error bounds. More explicitly, we propose an explicit generalization error upper bound for multilayer neural networks with $σ(0)=0$ and sufficiently broad Lipschitz loss functions, without requiring the width, depth, or other hyperparameters of the neural network to approach infinity, a specific neural network architecture (e.g., sparsity), or boundedness of the loss function, while also taking approximation error into consideration. In particular, we solve an open problem proposed by Weinan E et. al. in 2020 regarding the approximation rates in generalized Barron spaces. Furthermore, we show the near-minimax optimality of our theory for regression problems with ReLU activations. Notably, our upper bound exhibits the famous double descent phenomenon for such networks, which is the most distinguished characteristic compared with other existing results. Our subsequent work will prove the matching lower bounds in the minimax sense, meaning that it is highly possible that our theory reveals the true underlying mechanism of the double descent phenomenon. We can also explain scaling law from this theory.

cs.LG↗