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, point out pathologies in the approach, and propose an alternative parameterization of the Gaussian variational process using a continuous 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 the learning of model parameters.

翻译：扩散过程是一类随机微分方程（SDE），在动态建模任务中自然产生丰富的表达性模型族。在生成模型中，若潜过程以非线性扩散过程为先验，其概率推理与学习属于难以处理的问题。我们基于变分推断中以后验过程近似为线性扩散过程的研究工作，指出该方法的病理问题，并提出一种利用连续指数族描述的高斯变分过程替代参数化方案。这使得我们能够将依赖定点迭代的慢速推理算法，转化为类似自然梯度下降的凸优化快速算法，同时为模型参数的优化提供更优的目标函数。