Score-based generative models have recently achieved remarkable success. While they are usually parameterized by the score, an alternative way is to use a series of time-dependent energy-based models (EBMs), where the score is obtained from the negative input-gradient of the energy. Crucially, EBMs can be leveraged not only for generation, but also for tasks such as compositional sampling or building Boltzmann Generators via Monte Carlo methods. However, training EBMs remains challenging. Direct maximum likelihood is computationally prohibitive due to the need for nested sampling, while score matching, though efficient, suffers from mode blindness. To address these issues, we introduce the Diffusive Classification (DiffCLF) objective, a simple method that avoids blindness while remaining computationally efficient. DiffCLF reframes EBM learning as a supervised classification problem across noise levels, and can be seamlessly combined with standard score-based objectives. We validate the effectiveness of DiffCLF by comparing the estimated energies against ground truth in analytical Gaussian mixture cases, and by applying the trained models to tasks such as model composition and Boltzmann Generator sampling. Our results show that DiffCLF enables EBMs with higher fidelity and broader applicability than existing approaches.

翻译：基于分数的生成模型近期取得了显著成功。虽然它们通常通过分数进行参数化，但另一种方法是使用一系列时间依赖的基于能量的模型（EBMs），其中分数通过能量的负输入梯度获得。关键在于，EBMs不仅可用于生成，还可通过蒙特卡洛方法应用于组合采样或构建玻尔兹曼生成器等任务。然而，EBMs的训练仍然具有挑战性。直接的最大似然估计由于需要嵌套采样而在计算上不可行，而分数匹配虽然高效，却存在模态盲区问题。为解决这些问题，我们提出了扩散分类（DiffCLF）目标函数，这是一种避免盲区同时保持计算效率的简单方法。DiffCLF将EBM学习重新定义为跨噪声水平的监督分类问题，并且可以与标准的基于分数的目标函数无缝结合。我们通过在解析高斯混合案例中将估计能量与真实值进行比较，并将训练后的模型应用于模型组合和玻尔兹曼生成器采样等任务，验证了DiffCLF的有效性。我们的结果表明，与现有方法相比，DiffCLF能够实现具有更高保真度和更广泛适用性的EBMs。