  Time series forecasting has been a widely explored task of great importance
in many applications. However, it is common that real-world time series data
are recorded in a short time period, which results in a big gap between the
deep model and the limited and noisy time series. In this work, we propose to
address the time series forecasting problem with generative modeling and
propose a bidirectional variational auto-encoder (BVAE) equipped with
diffusion, denoise, and disentanglement, namely D3VAE. Specifically, a coupled
diffusion probabilistic model is proposed to augment the time series data
without increasing the aleatoric uncertainty and implement a more tractable
inference process with BVAE. To ensure the generated series move toward the
true target, we further propose to adapt and integrate the multiscale denoising
score matching into the diffusion process for time series forecasting. In
addition, to enhance the interpretability and stability of the prediction, we
treat the latent variable in a multivariate manner and disentangle them on top
of minimizing total correlation. Extensive experiments on synthetic and
real-world data show that D3VAE outperforms competitive algorithms with
remarkable margins. Our implementation is available at
https://github.com/PaddlePaddle/PaddleSpatial/tree/main/research/D3VAE.

Machine Learning