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Dynamical Diffusion: Learning Temporal Dynamics with Diffusion Models

ICLR 2025 · Time series › Causal and generative time series · approach: Diffusion models for time series · 0 citations (OpenAlex)

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Proposes Dynamical Diffusion (DyDiff), a diffusion framework whose forward and reverse processes mix historical states with noisy latents, applied to scientific spatiotemporal forecasting, video prediction, and time series forecasting.

Problem

Standard diffusion models used for temporal predictive learning treat prediction as conditional generation and do not explicitly model temporal dynamics in the diffusion process, which hurts temporal coherence of generated sequences.

Approach

Each diffusion latent at step t is defined as a timestep-aware mixture of the noisy current state and the previous latent (x_t^s = sqrt(gamma_bar)(sqrt(alpha_bar) x_0^s + noise) + sqrt(1-gamma_bar) x_t^{s-1}), with dependent noise across prediction steps; the marginal keeps the standard SNR so training uses the usual denoising objective via reparameterization.

Key results

On Turbulence Flow, DyDiff reduces CRPS from 0.0313 to 0.0275 (avg pooling) versus standard DPM, over 12% reduction.
On BAIR action-conditioned video prediction, DyDiff improves FVD from 48.5 to 45.0 over DPM.
On time series CRPS_sum, DyDiff outperforms TimeGrad with DPM on Solar (0.316 vs 0.372), Traffic, Taxi and Wikipedia.

Measured effects reported in the paper

What was changed	Where	Measured	Effect
Use DyDiff temporal dynamics instead of standard DPM	Scientific forecasting · SEVIR	CRPS avg: 8.67 -> 7.62	Helped
Use DyDiff temporal dynamics instead of standard DPM	Scientific forecasting · SEVIR	CSI: 0.285 -> 0.319	Helped
Use DyDiff temporal dynamics instead of standard DPM	Scientific forecasting · Turbulence Flow	CRPS avg: 0.0313 -> 0.0275	Helped
Use DyDiff temporal dynamics instead of standard DPM	Video prediction · BAIR action-free 64×64	FVD: 72.0 -> 67.4	Helped
Use DyDiff temporal dynamics instead of standard DPM	Video prediction · BAIR action-free 64×64	PSNR: 21.0 -> 21.0	No clear effect
Use DyDiff temporal dynamics instead of standard DPM	Video prediction · RoboNet action-free 64×64	FVD: 92.9 -> 81.7	Helped
Use DyDiff temporal dynamics instead of standard DPM	TimeGrad · Solar	Summed CRPS: 0.372_{\pm0.064} -> 0.316_{\pm0.010}	Helped
Use DyDiff temporal dynamics instead of standard DPM	TimeGrad · Electricity	Summed CRPS: 0.021_{\pm 0.002} -> 0.023_{\pm0.001}	Hurt
Use dependent noises instead of independent noises (ablation)	DyDiff · Predictive learning (Figure analysis)	performance	Helped
Set gamma-schedule factor η to 0.1, 0.5, or 0.9 rather than standard diffusion η=0 (ablation)	DyDiff · Turbulence Flow	performance	Helped
Set gamma-schedule factor η to 1.0 (ablation)	DyDiff · Turbulence Flow	performance	Hurt

Surprising findings

Using independent noises instead of dependent noises across prediction steps makes performance worse, even underperforming the baseline.
Setting the final gamma schedule value near zero (eta=1.0) significantly degrades performance and can underperform standard diffusion.

Limitations

Gains on some time series datasets (Exchange, Electricity) fall within baseline variance range.
On RoboNet, both DPM and DyDiff fall short of deterministic state-of-the-art methods.
Time series setup requires tuning of the gamma schedule (1-gamma_t = 0.3(1-alpha_t)) for stability.

Experimental setup

Datasets: Turbulence Flow SEVIR BAIR RoboNet Exchange Solar Electricity Traffic Taxi Wikipedia

Benchmarks: SEVIR Turbulence Flow BAIR RoboNet Exchange Solar Electricity Traffic Taxi Wikipedia

Metrics: CRPS CSI FVD PSNR SSIM LPIPS CRPS_sum

Baselines: DPM (standard diffusion) TimeGrad VideoGPT MaskViT FitVid MAGVIT iVideoGPT MCVD Transformer-MAF DeepAR

Builds on: DDPM DDIM Stable Video Diffusion TimeGrad

Closest papers by meaning

Why Diffusion Models Don’t Memorize: The Role of Implicit Dynamical Regularization in Training (NeurIPS 2025 · similarity 0.91)
Interacting Diffusion Processes for Event Sequence Forecasting (ICML 2024 · similarity 0.89)
ABC: Any-Subset Autoregression via Non-Markovian Diffusion Bridges in Continuous Time and Space (NeurIPS 2026 · similarity 0.89)
Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modelling (NeurIPS 2024 · similarity 0.88)
Tracing the Roots: Leveraging Temporal Dynamics in Diffusion Trajectories for Origin Attribution (NeurIPS 2025 · similarity 0.88)
TimeDART: A Diffusion Autoregressive Transformer for Self-Supervised Time Series Representation (ICML 2025 · similarity 0.88)

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