Variational autoencoders (VAEs) learn compact latent representations of complex data, but their generative capacity is fundamentally constrained by the choice of prior distribution over the latent space. Energy-based priors offer a principled way to move beyond factorized assumptions and capture structured interactions among latent variables, yet training such priors at scale requires accurate and efficient sampling from intractable distributions. Here we present Boltzmann-machine--prior VAEs (BM-VAEs) trained using quantum annealing--based sampling in three distinct operational modes within a single generative system. During training, diabatic quantum annealing (DQA) provides unbiased Boltzmann samples for gradient estimation of the energy-based prior; for unconditional generation, slower quantum annealing (QA) concentrates samples near low-energy minima; for conditional generation, bias fields are added to direct sampling toward attribute-specific regions of the energy landscape (c-QA). Using up to 2000 qubits on a D-Wave Advantage2 processor, we demonstrate stable and efficient training across multiple datasets, with faster convergence and lower reconstruction loss than a Gaussian-prior VAE. The learned Boltzmann prior enables unconditional generation by sampling directly from the energy-based latent distribution, a capability that plain autoencoders lack, and conditional generation through latent biasing that leverages the learned pairwise interactions.

翻译：变分自编码器（VAEs）能够学习复杂数据的紧凑潜在表征，但其生成能力从根本上受限于潜在空间先验分布的选择。基于能量的先验提供了一种超越因子化假设、捕捉潜在变量间结构化交互关系的严谨方法，然而大规模训练此类先验需要从难以处理的分布中进行准确且高效的采样。本文提出基于玻尔兹曼机先验的VAEs（BM-VAEs），在单一生成系统中采用三种不同运行模式下的量子退火采样进行训练。在训练阶段，非绝热量子退火（DQA）为能量基先验的梯度估计提供无偏玻尔兹曼样本；在无条件生成阶段，慢速量子退火（QA）将样本集中于低能量极小值附近；在条件生成阶段，通过添加偏置场引导采样指向能量景观中特定属性区域（c-QA）。利用D-Wave Advantage2处理器上多达2000个量子比特，我们在多个数据集上证明了稳定高效的训练过程，其收敛速度更快且重建损失低于高斯先验VAE。所学习的玻尔兹曼先验能够通过直接从能量基潜在分布中采样实现无条件生成（这是普通自编码器所不具备的能力），并可通过利用已学习的成对交互作用进行潜在偏置实现条件生成。