Aircraft manufacturing is the jewel in the crown of industry, among which generating high-fidelity airfoil geometries with controllable and editable representations remains a fundamental challenge. While existing deep-learning-based methods rely on predefined parametric function families, e.g., B\'ezier curves and discrete point-based representations, they suffer from inherent trade-offs between expressiveness and resolution flexibility. To tackle this challenge, we introduce FuncGenFoil, a novel function-space generative model that directly learns functional airfoil geometries. Our method inherits both the advantages of arbitrary resolution sampling and the smoothness of parametric functions, as well as the strong expressiveness of discrete point-based functions. Empirical evaluations on the AFBench dataset demonstrate that FuncGenFoil improves upon state-of-the-art methods in airfoil generation by achieving a relative -74.4 label error reduction and +23.2 diversity increase on the AF-200K dataset. Our results highlight the advantages of function-space modeling for aerodynamic shape optimization, offering a powerful and flexible framework for high-fidelity airfoil design. Our code will be released.

Generative models, particularly diffusion models, have achieved remarkable success in density estimation for multimodal data, drawing significant interest from the reinforcement learning (RL) community, especially in policy modeling in continuous action spaces. However, existing works exhibit significant variations in training schemes and RL optimization objectives, and some methods are only applicable to diffusion models. In this study, we compare and analyze various generative policy training and deployment techniques, identifying and validating effective designs for generative policy algorithms. Specifically, we revisit existing training objectives and classify them into two categories, each linked to a simpler approach. The first approach, Generative Model Policy Optimization (GMPO), employs a native advantage-weighted regression formulation as the training objective, which is significantly simpler than previous methods. The second approach, Generative Model Policy Gradient (GMPG), offers a numerically stable implementation of the native policy gradient method. We introduce a standardized experimental framework named GenerativeRL. Our experiments demonstrate that the proposed methods achieve state-of-the-art performance on various offline-RL datasets, offering a unified and practical guideline for training and deploying generative policies.

Recent generative models based on score matching and flow matching have significantly advanced generation tasks, but their potential in discriminative tasks remains underexplored. Previous approaches, such as generative classifiers, have not fully leveraged the capabilities of these models for discriminative tasks due to their intricate designs. We propose Pretrained Reversible Generation (PRG), which extracts unsupervised representations by reversing the generative process of a pretrained continuous flow model. PRG effectively reuses unsupervised generative models, leveraging their high capacity to serve as robust and generalizable feature extractors for downstream tasks. Our method consistently outperforms prior approaches across multiple benchmarks, achieving state-of-the-art performance among generative model-based methods, including 78\% top-1 accuracy on ImageNet. Extensive ablation studies further validate the effectiveness of our approach.