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：隐式动态模型常被用于学习表征噪声数据序列的隐式动态过程分布。然而，由于隐式状态与观测动态的复杂性与多变性，从这类模型生成高保真样本极具挑战性。近年来，基于扩散的生成模型（如DDPM和NCSN）在从先验分布生成高质量序列样本方面，为神经ODE、循环神经网络和归一化流网络等先进隐式生成模型提供了极具前景的替代方案，但其在隐式动态模型处理序列数据中的应用仍有待探索。本文提出一种新颖的隐式变量模型——隐式动态隐式扩散过程，该方法利用隐式扩散过程从动态隐式过程中采样，并据此生成序列观测样本。我们在合成数据与模拟神经解码问题中进行了测试，证明LDIDPs能够精准学习隐式维度的动态特征。此外，隐式采样方法支持从隐式空间与观测空间以计算高效的方式生成高质量序列数据样本。