analiza aiqbench
This paper gives statistical theory for Flow Matching, a generative modeling method that is becoming a simpler alternative to diffusion models. It argues that the kernel density estimator reaches the optimal Wasserstein convergence rate up to logarithmic factors, and that sufficiently large Flow Matching networks inherit this rate. It also shows faster rates when the data lies near a low-dimensional manifold, which offers a formal explanation for the method's empirical performance in high dimensions. For practitioners, the result is useful mainly as a justification for the approach, not a new training method, and its bounds apply under the paper's assumptions.
On the minimax optimality of Flow Matching through the connection to kernel density estimation
arXiv:2504.13336v3 Announce Type: replace-cross Abstract: Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models. While existing statistical guarantees adapt tools from the analysis of diffusion models, we take a different perspective by connecting Flow Matching to kernel density estimation. We first verify that the kernel density estimator matches the optimal rate of convergence in Wasserstein distance up to logarithmic factors, improving existing bounds for the Gaussian kernel. Based on this result, we prove that for sufficiently large networks, Flow Matching achieves the optimal rate up to logarithmic factors. If the target distribution lies on a lower-dimensional manifold, we show that the kernel density estimator profits from the smaller intrinsic dimension on a small tube around the manifold. The faster rate also applies to Flow Matching, providing a theoretical foundation for its empirical success in high-dimensional settings.
Abstract:Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models. While existing statistical guarantees adapt tools from the analysis of diffusion models, we take a different perspective by connecting Flow Matching to kernel density estimation. We first verify that the kernel density estimator matches the optimal rate of convergence in Wasserstein distance up to logarithmic factors, improving existing bounds for the Gaussian kernel. Based on this result, we prove that for sufficiently large networks, Flow Matching achieves the optimal rate up to logarithmic factors. If the target distribution lies on a lower-dimensional manifold, we show that the kernel density estimator profits from the smaller intrinsic dimension on a small tube around the manifold. The faster rate also applies to Flow Matching, providing a theoretical foundation for its empirical success in high-dimensional settings.
Machine Learning (stat.ML); Machine Learning (cs.LG); Statistics Theory (math.ST)
arXiv:2504.13336 [stat.ML]
(or arXiv:2504.13336v3 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2504.13336 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 238 cuvinte
Subiecte conexe
Optimization of Connection Patterns between Mobile Phones and Base Stations using Quantum Annealing
arXiv · 24 iul. 2026
Quantum networks can now optimize connections without full noise maps
Quantum Zeitgeist · 26 aug. 2026
Statistical Inference for Adversarial Training: Central Limit Theorems via Optimal Transport
arXiv · 22 sept. 2026
Discovery of connectivity-trainability trade-off of IQP circuits for Hamiltonian optimization
arXiv · 30 oct. 2026