aiqbench analysis
This paper establishes a rigorous quantitative framework for diffusion distillation, analyzing how local errors in flow maps amplify under stiff dynamics to inform optimal segmentation strategies. By proving score approximability and deriving explicit Lipschitz bounds within Gaussian mixture models, the authors provide theoretical certificates that guide efficient few-step sampling without relying on lower bound implications. The findings offer critical insights into balancing computational efficiency with stability when compressing complex diffusion trajectories.
A Quantitative Approximation Framework for Flow Distillation in Diffusion Models
arXiv:2606.03820v2 Announce Type: replace-cross Abstract: We develop a quantitative framework for diffusion distillation by viewing few step sampling as approximation through compositions of learned flow maps. For trajectory distillation of the probability flow ODE, we show that low noise multimodal regimes separate score approximability from dynamical stability: the score remains efficiently approximable, while small local errors may be strongly amplified by stiff flow dynamics. In a Gaussian mixture Ornstein--Uhlenbeck model, we prove time uniform \(L^p(p_t)\) score approximation by ReLU and ReQU networks with explicit polylogarithmic complexity, and derive a computable Lipschitz bound \(L(t)\) for the flow velocity. The stability factor \(\exp\bigl(\int_s^t L(u)\mathrm du\bigr)\) can grow exponentially as noise decreases and mixture separation increases. Comparing this certificate with a certified local Lipschitz budget for one step students identifies regimes of direct distillation difficulty, without implying an approximation lower bound. We also show that deep residual compositions control global transport error through propagated local errors, and that equalizing cumulative stability yields an optimal nonuniform segmentation. With eight segments, this grid reduces final mean relative MSE by up to \(51.9\%\) versus uniform grids.
Abstract:We develop a quantitative framework for diffusion distillation by viewing few step sampling as approximation through compositions of learned flow maps. For trajectory distillation of the probability flow ODE, we show that low noise multimodal regimes separate score approximability from dynamical stability: the score remains efficiently approximable, while small local errors may be strongly amplified by stiff flow dynamics. In a Gaussian mixture Ornstein--Uhlenbeck model, we prove time uniform \(L^p(p_t)\) score approximation by ReLU and ReQU networks with explicit polylogarithmic complexity, and derive a computable Lipschitz bound \(L(t)\) for the flow velocity. The stability factor \(\exp\bigl(\int_s^t L(u)\mathrm du\bigr)\) can grow exponentially as noise decreases and mixture separation increases. Comparing this certificate with a certified local Lipschitz budget for one step students identifies regimes of direct distillation difficulty, without implying an approximation lower bound. We also show that deep residual compositions control global transport error through propagated local errors, and that equalizing cumulative stability yields an optimal nonuniform segmentation. With eight segments, this grid reduces final mean relative MSE by up to \(51.9\%\) versus uniform grids.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2606.03820 [stat.ML]
(or arXiv:2606.03820v2 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2606.03820 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 270 words
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