Towards High-Order Mean Flow Generative Models: Feasibility, Expressivity, and Provably Efficient Criteria
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908483789520896 |
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| author | Cao, Yang Chen, Yubin Song, Zhao Zhang, Jiahao |
| author_facet | Cao, Yang Chen, Yubin Song, Zhao Zhang, Jiahao |
| contents | Generative modelling has seen significant advances through simulation-free paradigms such as Flow Matching, and in particular, the MeanFlow framework, which replaces instantaneous velocity fields with average velocities to enable efficient single-step sampling. In this work, we introduce a theoretical study on Second-Order MeanFlow, a novel extension that incorporates average acceleration fields into the MeanFlow objective. We first establish the feasibility of our approach by proving that the average acceleration satisfies a generalized consistency condition analogous to first-order MeanFlow, thereby supporting stable, one-step sampling and tractable loss functions. We then characterize its expressivity via circuit complexity analysis, showing that under mild assumptions, the Second-Order MeanFlow sampling process can be implemented by uniform threshold circuits within the $\mathsf{TC}^0$ class. Finally, we derive provably efficient criteria for scalable implementation by leveraging fast approximate attention computations: we prove that attention operations within the Second-Order MeanFlow architecture can be approximated to within $1/\mathrm{poly}(n)$ error in time $n^{2+o(1)}$. Together, these results lay the theoretical foundation for high-order flow matching models that combine rich dynamics with practical sampling efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07102 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards High-Order Mean Flow Generative Models: Feasibility, Expressivity, and Provably Efficient Criteria Cao, Yang Chen, Yubin Song, Zhao Zhang, Jiahao Machine Learning Artificial Intelligence Computer Vision and Pattern Recognition Generative modelling has seen significant advances through simulation-free paradigms such as Flow Matching, and in particular, the MeanFlow framework, which replaces instantaneous velocity fields with average velocities to enable efficient single-step sampling. In this work, we introduce a theoretical study on Second-Order MeanFlow, a novel extension that incorporates average acceleration fields into the MeanFlow objective. We first establish the feasibility of our approach by proving that the average acceleration satisfies a generalized consistency condition analogous to first-order MeanFlow, thereby supporting stable, one-step sampling and tractable loss functions. We then characterize its expressivity via circuit complexity analysis, showing that under mild assumptions, the Second-Order MeanFlow sampling process can be implemented by uniform threshold circuits within the $\mathsf{TC}^0$ class. Finally, we derive provably efficient criteria for scalable implementation by leveraging fast approximate attention computations: we prove that attention operations within the Second-Order MeanFlow architecture can be approximated to within $1/\mathrm{poly}(n)$ error in time $n^{2+o(1)}$. Together, these results lay the theoretical foundation for high-order flow matching models that combine rich dynamics with practical sampling efficiency. |
| title | Towards High-Order Mean Flow Generative Models: Feasibility, Expressivity, and Provably Efficient Criteria |
| topic | Machine Learning Artificial Intelligence Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2508.07102 |