DynG-Diff: A State-Aware Dynamic Guidance Diffusion Framework for Probabilistic Time Series Forecasting

Multivariate time series imputation (MTSI) aims to recover missing values in temporal data composed of multiple interdependent variables. This problem is central to real-world applications such as healthcare monitoring, traffic networks, and energy systems. Recent diffusion-based approaches have shown strong potential for probabilistic imputation by learning to generate missing values through iterative denoising. However, most existing approaches perform diffusion directly in the original data space, requiring the denoising network to simultaneously capture global structure, temporal dynamics, and stochastic variability. This makes the generative task unnecessarily complex, especially when modern deterministic imputers can already provide accurate initial reconstructions. To address this limitation, we propose RDDMPI, a conditional residual diffusion framework that operates directly in residual space. Instead of modeling the full missing signal directly, we reformulate probabilistic imputation as a baseline-residual decomposition, where a pretrained model captures the dominant signal and a diffusion process models the residual uncertainty. To better exploit deterministic guidance, \model{} conditions the reverse denoising process on both the baseline-completed signal and its latent representation, while a reliability-aware conditioning mechanism adaptively controls the influence of baseline information during residual generation. This formulation simplifies the diffusion learning objective, enabling it to focus on structured correction terms rather than reconstructing the full signal. Experiments on multiple benchmark datasets demonstrate that RDDMPI consistently improves both reconstruction accuracy and uncertainty quantification.

In many domains, practitioners seek models that produce accurate forecasts while faithfully capturing latent system dynamics. Existing approaches typically sacrifice one of these goals: deep state space models often assume Gaussian latent transitions, limiting fit and forecasting, while diffusion models are highly expressive but lack principled inference for the underlying dynamics. To combine the strengths of both, we introduce the Diffusion-Driven State Space Model (DDSSM), which replaces the conventional Gaussian transition distribution with a diffusion model. Our DDSSM resolves the open problem of how to jointly train an autoencoder and a diffusion model on sequential data, thereby extending the literature on latent diffusion models for time series. Moreover, we find that the DDSSM empirically outperforms a state-of-the-art deep SSM at fitting and forecasting a simulated time series with multimodal transitions.

Effectively modeling non-stationary dynamics in probabilistic multivariate time series(MTS) forecasting requires balancing expressiveness with robustness. Existing parametric approaches benefit from strong inductive biases but lack flexibility, whereas deep generative models struggle to capture complex temporal dependencies without extensive data and computation. We introduce Parametric Prior Mapping (PPM), a framework that injects parametric structural priors into a generative modeling process. Specifically, PPM utilizes a parametric estimator to derive a dynamic, adaptive prior that guides the learning of a complex predictive distribution via a learnable mapping. This design allows the model to retain the efficiency of parametric methods while exploiting the expressive power of generative models. Trained with a hybrid objective, PPM yields precise forecasts with well-calibrated uncertainty estimates. Empirical results show that PPM outperforms existing baselines in handling non-stationary data, offering a superior trade-off between accuracy and computational efficiency. The code is available at https://github.com/ljl8336/PPM.