  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.
