Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with latent processes endowed with a non-linear diffusion process prior are intractable problems. We build upon work within variational inference, approximating the posterior process as a linear diffusion process, and point out pathologies in the approach. We propose an alternative parameterization of the Gaussian variational process using a site-based exponential family description. This allows us to trade a slow inference algorithm with fixed-point iterations for a fast algorithm for convex optimization akin to natural gradient descent, which also provides a better objective for learning model parameters.

翻译：扩散过程是一类随机微分方程，在动态建模任务中自然衍生出丰富且富有表现力的模型族。当生成模型中的潜在过程以非线性扩散过程为先验时，其概率推断与学习属于难以处理的问题。我们基于变分推断领域的研究工作，将后验过程近似为线性扩散过程，并指出该方法中存在的病态问题。我们提出一种利用基于位点的指数族描述的高斯变分过程替代参数化方案。通过以定点迭代实现的慢速推断算法，我们可将其替换为类似自然梯度下降的凸优化快速算法，该算法同时为学习模型参数提供了更优的目标函数。