Recent work shows that path gradient estimators for normalizing flows have lower variance compared to standard estimators, resulting in improved training. However, they are often prohibitively more expensive from a computational point of view and cannot be applied to maximum likelihood training in a scalable manner, which severely hinders their widespread adoption. In this work, we overcome these crucial limitations. Specifically, we propose a fast path gradient estimator which works for all normalizing flow architectures of practical relevance for sampling from an unnormalized target distribution. We then show that this estimator can also be applied to maximum likelihood training and empirically establish its superior performance for several natural sciences applications.

Generative modeling via stochastic processes has led to remarkable empirical results as well as to recent advances in their theoretical understanding. In principle, both space and time of the processes can be discrete or continuous. In this work, we study time-continuous Markov jump processes on discrete state spaces and investigate their correspondence to state-continuous diffusion processes given by SDEs. In particular, we revisit the $\textit{Ehrenfest process}$, which converges to an Ornstein-Uhlenbeck process in the infinite state space limit. Likewise, we can show that the time-reversal of the Ehrenfest process converges to the time-reversed Ornstein-Uhlenbeck process. This observation bridges discrete and continuous state spaces and allows to carry over methods from one to the respective other setting, such as for instance loss functions that lead to improved convergence. Additionally, we suggest an algorithm for training the time-reversal of Markov jump processes which relies on conditional expectations and can thus be directly related to denoising score matching. We demonstrate our methods in multiple convincing numerical experiments.

Drone-based aerial thermography has become a convenient quality assessment tool for the precise localization of defective modules and cells in large photovoltaic-power plants. However, manual evaluation of aerial infrared recordings can be extremely time-consuming. Therefore, we propose an approach for automatic detection and analysis of photovoltaic modules in aerial infrared images. Significant temperature abnormalities such as hot spots and hot areas can be identified using our processing pipeline. To identify such defects, we first detect the individual modules in infrared images, and then use statistical tests to detect the defective modules. A quantitative evaluation of the detection and analysis pipeline on real-world, infrared recordings shows the applicability of our approach.