变分薛定谔扩散模型
Variational Schrödinger Diffusion Models
AI总结：
提出变分薛定谔扩散模型，通过变分推断线性化向前得分，实现无模拟训练，提升生成效率与可扩展性，并在CIFAR10和时间序列任务上验证性能。
摘要：
薛定谔桥（SB）已成为扩散模型中优化传输计划的首选方法。然而，SB需要估计难以处理的向前得分函数，这不可避免地导致基于模拟轨迹的高成本隐式训练损失。为了提高可扩展性同时保留高效的传输计划，我们利用变分推断将SB的向前得分函数线性化（变分得分），并恢复训练向后得分时的无模拟特性。我们提出了变分薛定谔扩散模型（VSDM），其中向前过程是多元扩散，变分得分被自适应优化以实现高效传输。理论上，我们使用随机逼近证明变分得分的收敛性，并展示基于最优变分得分自适应生成样本的收敛性。实证上，我们在模拟示例中测试算法，观察到VSDM在生成各向异性形状时高效，并产生比单变量扩散更直的样本轨迹。我们还验证了算法在真实数据上的可扩展性，在CIFAR10上实现了具有竞争力的无条件生成性能，并在时间序列建模中实现了条件生成。值得注意的是，VSDM不再依赖预热初始化，在大规模实验训练中变得易于调参。
英文摘要：
Schrödinger bridge (SB) has emerged as the go-to method for optimizing transportation plans in diffusion models. However, SB requires estimating the intractable forward score functions, inevitably resulting in the costly implicit training loss based on simulated trajectories. To improve the scalability while preserving efficient transportation plans, we leverage variational inference to linearize the forward score functions (variational scores) of SB and restore simulation-free properties in training backward scores. We propose the variational Schrödinger diffusion model (VSDM), where the forward process is a multivariate diffusion and the variational scores are adaptively optimized for efficient transport. Theoretically, we use stochastic approximation to prove the convergence of the variational scores and show the convergence of the adaptively generated samples based on the optimal variational scores. Empirically, we test the algorithm in simulated examples and observe that VSDM is efficient in generations of anisotropic shapes and yields straighter sample trajectories compared to the single-variate diffusion. We also verify the scalability of the algorithm in real-world data and achieve competitive unconditional generation performance in CIFAR10 and conditional generation in time series modeling. Notably, VSDM no longer depends on warm-up initializations and has become tuning-friendly in training large-scale experiments.
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