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The paper introduces a divergence-kernel method for jointly training neural SDE drift and diffusion fields with losses that depend directly on the terminal density, achieving fewer off-mode samples than score-based generators on Gaussian-mixture benchmarks with time-independent fields.
StochLOB 提出一种仅在训练阶段使用的评分匹配框架，用跳跃 Lévy 噪声和截断 α-stable 噪声替代布朗高斯扩散污染，以更真实地刻画限价订单簿数据的重尾与跳跃特性，从而提升 BTC 及山寨币中价趋势预测在压力窗口下的稳健性。
A theoretical study of denoising score matching showing how rank constraints and architectural bottlenecks in score networks affect generalization, deriving asymptotically precise training and test errors via truncated SVD in a random-feature model and identifying a natural rank threshold tied to the data subspace's orthogonal complement.
This paper connects score matching, maximum likelihood, and expectation-maximization in mixed linear regression, providing theoretical guarantees and analyzing gradient behavior under diffusion noise levels.
This paper identifies a collapse-and-refine mechanism in diffusion models under the manifold hypothesis, proposing Score-induced Latent Diffusion (SiLD) that provably avoids the curse of dimensionality. Experiments show SiLD matches or outperforms VAE-based latent diffusion models.
This paper provides the first non-asymptotic sample complexity bounds for learning exponential families of polynomials with score matching, showing polynomial dependence on model dimension.