aiqbench analysis
This paper advances theoretical understanding of one-step generative modeling by deriving convergence rates for finite-particle drifting models under specific regularity and stability assumptions. It establishes rigorous bounds for smoothed Fisher discrepancy and particle velocity, highlighting divergence risks in shrinking-bandwidth regimes while providing explicit correction terms for unbounded empirical scales. These findings offer critical mathematical grounding for improving the accuracy and stability of next-generation diffusion-based generative architectures.
Finite-Particle Convergence Rates for Conservative and Non-Conservative Drifting Models
arXiv:2605.22795v3 Announce Type: replace-cross Abstract: We analyze finite-particle drifting models for one-step generative modeling. For a conservative velocity given by the difference of the kernel-smoothed data and model scores, a joint-entropy identity yields continuous-time bounds for the smoothed Fisher discrepancy and the squared particle velocity. The finite-particle correction involves reciprocal kernel density estimates. We give local-occupancy conditions and exact expectation bounds, and show that these expectations diverge for full-support initial densities in a shrinking-bandwidth regime. Keeping the bandwidth dependence of the quadrature constants explicit yields a conditional root residual-velocity rate of $N^{-1/(d+4)}$ under uniform regularity, with a corresponding rate under weaker quadrature growth conditions. We also analyze the original displacement field with the exact Laplace kernel. A companion kernel gives a weighted coercivity estimate that accommodates the unbounded empirical scale and the kernel's nondifferentiability. Localization controls the particle velocity, while relative scale alignment absorbs the mismatch into dissipation. Both analyses quantify the size of an additional drift correction under explicit regularity and stability assumptions.
Abstract:We analyze finite-particle drifting models for one-step generative modeling. For a conservative velocity given by the difference of the kernel-smoothed data and model scores, a joint-entropy identity yields continuous-time bounds for the smoothed Fisher discrepancy and the squared particle velocity. The finite-particle correction involves reciprocal kernel density estimates. We give local-occupancy conditions and exact expectation bounds, and show that these expectations diverge for full-support initial densities in a shrinking-bandwidth regime. Keeping the bandwidth dependence of the quadrature constants explicit yields a conditional root residual-velocity rate of $N^{-1/(d+4)}$ under uniform regularity, with a corresponding rate under weaker quadrature growth conditions. We also analyze the original displacement field with the exact Laplace kernel. A companion kernel gives a weighted coercivity estimate that accommodates the unbounded empirical scale and the kernel's nondifferentiability. Localization controls the particle velocity, while relative scale alignment absorbs the mismatch into dissipation. Both analyses quantify the size of an additional drift correction under explicit regularity and stability assumptions.
Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Statistics Theory (math.ST)
arXiv:2605.22795 [stat.ML]
(or arXiv:2605.22795v3 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2605.22795 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 260 words
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