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Analysis of learning a flow-based generative model from limited sample complexity

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arxiv 2310.03575 v2 pith:CUTFIRWC submitted 2023-10-05 stat.ML cs.LG

classification stat.MLcs.LG
keywords analysisgenerativemixturetargetclosed-formdensityflow-basedgaussian
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abstract

We study the problem of training a flow-based generative model, parametrized by a two-layer autoencoder, to sample from a high-dimensional Gaussian mixture. We provide a sharp end-to-end analysis of the problem. First, we provide a tight closed-form characterization of the learnt velocity field, when parametrized by a shallow denoising auto-encoder trained on a finite number $n$ of samples from the target distribution. Building on this analysis, we provide a sharp description of the corresponding generative flow, which pushes the base Gaussian density forward to an approximation of the target density. In particular, we provide closed-form formulae for the distance between the mean of the generated mixture and the mean of the target mixture, which we show decays as $\Theta_n(\frac{1}{n})$. Finally, this rate is shown to be in fact Bayes-optimal.

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Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Classifier-Free Guidance: From High-Dimensional Analysis to Generalized Guidance Forms

    cs.LG 2025-02 conditional novelty 7.0 of 10

    CFG's distortion of the target distribution vanishes as data dimension grows, and a power-law generalization improves fidelity and diversity in high-dimensional generative models.

  2. Bigger Isn't Always Memorizing: Early Stopping Overparameterized Diffusion Models

    cs.LG 2025-05 conditional novelty 6.0 of 10

    In overparameterized diffusion models, generalization happens first and memorization starts later, with the memorization time growing linearly with dataset size.

  3. Provable diffusion-based posterior sampling for linear inverse problems via DDIM

    cs.LG 2026-07 reject novelty 5.0 of 10

    A SVD-based, coordinate-wise DDIM sampler is claimed to asymptotically sample from the posterior for noisy linear inverse problems, but the proof's posterior identification step does not follow from the stated updates.

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