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RDPI: A Refine Diffusion Probability Generation Method for Spatiotemporal Data Imputation
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Proposes RDPI, a two-stage spatiotemporal imputation method that refines a deterministic (GRIN-based) initial imputation with a conditional diffusion model that models residuals and injects observed values into the forward process.
Problem
Spatiotemporal data imputation for sensor data with temporal and spatial missingness; autoregressive methods accumulate errors and standard conditional diffusion models (e.g., CSDI) use observed conditions only in training and denoising, not in the forward process.
Approach
Two-stage framework: a deterministic initial imputer (GRIN) provides rough estimates, and a conditional diffusion model learns the residual between the estimate and ground truth, with observed values incorporated into the forward diffusion process and a derived ELBO; accelerated sampling keeps the random component.
Key results
- On AQI36 in-sample, RDPI reaches MAE 7.98 and MSE 238.25 versus MIDM's 9.41 and 361.28 and GRIN's 10.51 and 371.47.
- On PEMS-BAY block-missing, RDPI achieves MAE 0.90 versus 1.03 for MIDM and 1.14 for GRIN.
- On METR-LA block-missing, RDPI achieves MAE 1.96 versus 2.03 for GRIN, and the paper reports the best results across the four datasets.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add the RDPI two-stage conditional residual-diffusion method | GRIN-based imputation · AQI36 In-sample | MAE: 9.41$\pm$0.20 -> 7.98$\pm$0.24 | Helped |
| add the RDPI two-stage conditional residual-diffusion method | GRIN-based imputation · AQI In-sample | MAE: 10.06$\pm$0.11 -> 9.10$\pm$0.33 | Helped |
| add the RDPI two-stage conditional residual-diffusion method | GRIN-based imputation · PEMS-BAY Block-missing | MAE: 1.03$\pm$0.01 -> 0.90$\pm$0.01 | Helped |
| add the RDPI two-stage conditional residual-diffusion method | GRIN-based imputation · METR-LA Point-missing | MAE: 1.79$\pm$0.00 -> 1.73$\pm$0.01 | Helped |
| add observed-value conditioning to the forward process (ablation) | RDPI · METR-LA Block-missing | MAE: 2.05$\pm$0.01 -> 1.96$\pm$0.01 | Helped |
| use residuals as the diffusion target (ablation) | RDPI · METR-LA Block-missing | MAE: 1.97$\pm$0.01 -> 1.96$\pm$0.01 | Helped |
| jointly train the initial and denoising models (ablation) | RDPI · METR-LA Block-missing | MAE: 2.04$\pm$0.01 -> 1.96$\pm$0.01 | Helped |
| pretrain the initial model (ablation) | RDPI · METR-LA Block-missing | MAE: 2.12$\pm$0.01 -> 1.96$\pm$0.01 | Helped |
| predict εθ rather than xθ (ablation) | RDPI · METR-LA Block-missing | MAE: 1.97$\pm$0.04 -> 1.96$\pm$0.01 | Helped |
| use fθ(x₀ᶜ) − x₀ᵐ as the residual target rather than x₀ᵐ − fθ(x₀ᶜ) (ablation) | RDPI · METR-LA Block-missing | MAE: 2.63$\pm$0.02 -> 1.96$\pm$0.01 | Helped |
Surprising findings
- Predicting x0 instead of noise performs worse, which the authors attribute to a low signal-to-noise ratio in the residual target.
- Using the loss ||f(x_c) - x_m|| instead of ||x_m - f(x_c)|| makes the initial model's error grow as the diffusion loss decreases, destabilizing training.
Limitations
- Evaluated only on spatiotemporal traffic and air quality data; the authors note the method is tested mainly on traffic imputation.
- MRE does not improve consistently, and the authors attribute this to the smoothing effect of the diffusion model without fully validating it.
- Hyperparameters are set empirically per dataset, and the paper notes larger values are not always better.
Experimental setup
Datasets: PEMS-BAY METR-LA AQI AQI36
Benchmarks: PEMS-BAY METR-LA AQI AQI36
Metrics: MAE MSE MRE
Baselines: MEAN KNN MICE VAR BRITS GRIN GP-VAE CSDI MIDM
Builds on: CSDI GRIN DDPM DDIM
Closest papers by meaning
- Diffusion Transformers for Imputation: Statistical Efficiency and Uncertainty Quantification (NeurIPS 2025 · similarity 0.90)
- Learning from Highly Sparse Spatio-temporal Data (NeurIPS 2024 · similarity 0.89)
- Causal Deciphering and Inpainting in Spatio-Temporal Dynamics via Diffusion Model (NeurIPS 2024 · similarity 0.88)
- Graph Structure Learning for Spatial-Temporal Imputation: Adapting to Node and Feature Scales (AAAI 2025 · similarity 0.88)
- ProCTI: Prototype-Refined Global Conditioning for Diffusion-Based Time Series Imputation (NeurIPS 2026 · similarity 0.87)
- Self-attention-based Diffusion Model for Time-series Imputation in Partial Blackout Scenarios (AAAI 2025 · similarity 0.86)
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