Latent dynamical models are commonly used to learn the distribution of a latent dynamical process that represents a sequence of noisy data samples. However, producing samples from such models with high fidelity is challenging due to the complexity and variability of latent and observation dynamics. Recent advances in diffusion-based generative models, such as DDPM and NCSN, have shown promising alternatives to state-of-the-art latent generative models, such as Neural ODEs, RNNs, and Normalizing flow networks, for generating high-quality sequential samples from a prior distribution. However, their application in modeling sequential data with latent dynamical models is yet to be explored. Here, we propose a novel latent variable model named latent dynamical implicit diffusion processes (LDIDPs), which utilizes implicit diffusion processes to sample from dynamical latent processes and generate sequential observation samples accordingly. We tested LDIDPs on synthetic and simulated neural decoding problems. We demonstrate that LDIDPs can accurately learn the dynamics over latent dimensions. Furthermore, the implicit sampling method allows for the computationally efficient generation of high-quality sequential data samples from the latent and observation spaces.

翻译：潜变量动力学模型常用于学习表征一系列含噪数据样本的潜动态过程分布。然而，由于潜变量和观测动力学的复杂性与多变性，生成此类模型的高保真样本具有挑战性。近期基于扩散的生成模型（如DDPM和NCSN）已展现出作为新兴替代方案的潜力，能够从先验分布中生成高质量序列样本，性能优于神经ODE、RNN和标准化流网络等当前最优潜变量生成模型。但这类模型在潜变量动力学框架下进行序列数据建模的应用仍有待探索。本文提出名为隐式动态扩散过程的潜变量动力学模型（LDIDPs），该模型利用隐式扩散过程从动态潜变量过程中采样，并相应生成序列观测样本。我们基于合成数据与模拟神经解码问题测试LDIDPs，证明其能精确学习潜维度上的动力学特征。此外，隐式采样方法可在计算高效的同时，从潜变量空间和观测空间生成高质量序列数据样本。