Learning Energy-Based Generative Models via Potential Flow: A Variational Principle Approach to Probability Density Homotopy Matching

Energy-based models (EBMs) are a powerful class of probabilistic generative models due to their flexibility and interpretability. However, relationships between potential flows and explicit EBMs remain underexplored, while contrastive divergence training via implicit Markov chain Monte Carlo (MCMC) sampling is often unstable and expensive in high-dimensional settings. In this paper, we propose Variational Potential Flow Bayes (VPFB), a new energy-based generative framework that eliminates the need for implicit MCMC sampling and does not rely on auxiliary networks or cooperative training. VPFB learns an energy-parameterized potential flow by constructing a flow-driven density homotopy that is matched to the data distribution through a variational loss minimizing the Kullback-Leibler divergence between the flow-driven and marginal homotopies. This principled formulation enables robust and efficient generative modeling while preserving the interpretability of EBMs. Experimental results on image generation, interpolation, out-of-distribution detection, and compositional generation confirm the effectiveness of VPFB, showing that our method performs competitively with existing approaches in terms of sample quality and versatility across diverse generative modeling tasks.

Variational Potential Flow: A Novel Probabilistic Framework for Energy-Based Generative Modelling

Energy based models (EBMs) are appealing for their generality and simplicity in data likelihood modeling, but have conventionally been difficult to train due to the unstable and time-consuming implicit MCMC sampling during contrastive divergence training. In this paper, we present a novel energy-based generative framework, Variational Potential Flow (VAPO), that entirely dispenses with implicit MCMC sampling and does not rely on complementary latent models or cooperative training. The VAPO framework aims to learn a potential energy function whose gradient (flow) guides the prior samples, so that their density evolution closely follows an approximate data likelihood homotopy. An energy loss function is then formulated to minimize the Kullback-Leibler divergence between density evolution of the flow-driven prior and the data likelihood homotopy. Images can be generated after training the potential energy, by initializing the samples from Gaussian prior and solving the ODE governing the potential flow on a fixed time interval using generic ODE solvers. Experiment results show that the proposed VAPO framework is capable of generating realistic images on various image datasets. In particular, our proposed framework achieves competitive FID scores for unconditional image generation on the CIFAR-10 and CelebA datasets.

MDHA: Multi-Scale Deformable Transformer with Hybrid Anchors for Multi-View 3D Object Detection

Multi-view 3D object detection is a crucial component of autonomous driving systems. Contemporary query-based methods primarily depend either on dataset-specific initialization of 3D anchors, introducing bias, or utilize dense attention mechanisms, which are computationally inefficient and unscalable. To overcome these issues, we present MDHA, a novel sparse query-based framework, which constructs adaptive 3D output proposals using hybrid anchors from multi-view, multi-scale input. Fixed 2D anchors are combined with depth predictions to form 2.5D anchors, which are projected to obtain 3D proposals. To ensure high efficiency, our proposed Anchor Encoder performs sparse refinement and selects the top-k anchors and features. Moreover, while existing multi-view attention mechanisms rely on projecting reference points to multiple images, our novel Circular Deformable Attention mechanism only projects to a single image but allows reference points to seamlessly attend to adjacent images, improving efficiency without compromising on performance. On the nuScenes val set, it achieves 46.4% mAP and 55.0% NDS with a ResNet101 backbone. MDHA significantly outperforms the baseline, where anchor proposals are modelled as learnable embeddings.