Cox processes model overdispersed point process data via a latent stochastic intensity, but both nonparametric estimation of the intensity model and posterior inference over intensity paths are typically intractable, relying on expensive MCMC methods. We introduce Neural Diffusion Intensity Models, a variational framework for Cox processes driven by neural SDEs. Our key theoretical result, based on enlargement of filtrations, shows that conditioning on point process observations preserves the diffusion structure of the latent intensity with an explicit drift correction. This guarantees the variational family contains the true posterior, so that ELBO maximization coincides with maximum likelihood estimation under sufficient model capacity. We design an amortized encoder architecture that maps variable-length event sequences to posterior intensity paths by simulating the drift-corrected SDE, replacing repeated MCMC runs with a single forward pass. Experiments on synthetic and real-world data demonstrate accurate recovery of latent intensity dynamics and posterior paths, with orders-of-magnitude speedups over MCMC-based methods.

翻译：Cox过程通过潜在随机强度建模过分散的点过程数据，但强度模型的非参数估计及强度路径的后验推断通常难以处理，需依赖昂贵的MCMC方法。本文提出神经扩散强度模型——一种由神经随机微分方程驱动的Cox过程变分推断框架。基于滤波扩张的核心理论结果表明，在点过程观测条件下，潜在强度的扩散结构得以保持并具有显式漂移校正。这保证了变分族包含真实后验分布，使得在模型容量充足时ELBO最大化等价于极大似然估计。我们设计了一种摊销编码器架构，通过模拟漂移校正的随机微分方程，将变长事件序列映射为后验强度路径，从而用单次前向传播替代重复的MCMC计算。在合成数据与真实数据上的实验表明，该方法能精确还原潜在强度动态与后验路径，较基于MCMC的方法实现数量级的速度提升。