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.

本文提出了一种名为 LDIDPs 的新型隐式扩散过程潜在动态变量模型，它利用隐式扩散过程对潜在动态过程进行采样，并相应地产生连续观测样本，LDIDPs 成功地在合成和仿真神经解码问题上得到了测试，并展示了其能够在潜在尺寸上准确地学习动态，同时其隐式采样方法允许高效地从潜在和观测空间生成高质量的连续数据样本。