🧬 biology

Generative diffusion models for spatiotemporal influenza forecasting

The paper introduces Influpaint, a generative diffusion model that frames influenza forecasting as a spatiotemporal inpainting task to effectively capture complex epidemic dynamics and multimodal uncertainty, achieving competitive accuracy in both retrospective and real-time CDC FluSight challenges.

Original authors: Joseph Lemaitre, Justin Lessler

Published 2026-04-29

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Joseph Lemaitre, Justin Lessler

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Imagine trying to predict the path of a storm. You can't just look at the wind right now; you need to understand how storms have behaved in the past, how they might change, and what a "typical" storm looks like versus a "wild" one.

This paper introduces a new tool called Influpaint, which uses a type of advanced artificial intelligence (called a "diffusion model") to predict how flu seasons will unfold across the United States.

Here is how it works, explained simply:

1. The "Flu Map" Picture

Instead of looking at flu data as a long list of numbers or a spreadsheet, Influpaint turns the entire flu season into a single, giant picture.

The X-axis (Left to Right): Represents time (the 52 weeks of a year).
The Y-axis (Top to Bottom): Represents location (all 50 states and Washington D.C.).
The Colors: The brightness of the pixels represents how many people are getting sick. A bright white spot means a lot of flu cases; a dark spot means very few.

Think of it like a weather map, but instead of showing rain clouds, it shows "flu clouds" moving across the country over time.

2. The "Denoising" Magic

The AI behind Influpaint is trained like an artist learning to restore a damaged painting.

The Training: The researchers showed the AI thousands of "pictures" of flu seasons. Some were real data from hospitals, and others were "fake" seasons created by computer simulations.
The Process: The AI learns to take a picture that has been completely scrambled with static (like TV snow) and slowly "denoise" it until a clear, realistic flu season emerges. It learns the rules of how flu usually spreads: when it starts, how fast it grows, where it peaks, and how it fades away.

3. The "Inpainting" Forecast

This is the clever part. Usually, AI generates a whole new picture from scratch. But for forecasting, we already know what happened in the past few weeks.

The Scenario: Imagine you have a photo of a flu season, but the future part of the photo is torn off or covered in static. You can see the first few weeks clearly, but the rest is missing.
The Fix: Influpaint uses a technique called inpainting. It looks at the clear, known weeks (the past) and uses its training to "paint in" the missing future weeks. It doesn't just guess one future; it generates 512 different possible futures (like 512 different artists painting the same scene).
The Result: You get a "fan" of possibilities. Some show a huge spike in flu, some show a small one, and some show it hitting early or late. This gives public health officials a range of realistic scenarios rather than a single, brittle prediction.

4. What the Paper Found

The authors tested this tool in real-world competitions (called FluSight) where different teams try to predict flu trends.

Realism: When asked to generate a whole flu season from scratch (without any real data), Influpaint created seasons that looked very real, including complex patterns like double peaks (two waves of flu in one season).
Accuracy: In the 2024–2025 flu season, Influpaint became one of the top-performing models, beating many traditional methods. It was very good at predicting how high the flu would get and when it would peak.
The Secret Sauce: The AI worked best when it was trained on a mix of 30% real hospital data and 70% computer simulations. It turns out, the AI needed to see many "what-if" scenarios (simulations) to learn how to handle the uncertainty of the future, even though real data is more accurate.
A Flaw: While the predictions were very sharp and accurate, the AI was sometimes too confident. It drew a tight circle around its prediction, but the real flu numbers sometimes fell just outside that circle. It knew what would happen, but it underestimated how much it might be wrong.

5. Why This Matters

The paper claims that this is the first time this specific type of AI (diffusion models) has been used for disease forecasting.

Flexibility: Because it treats the data like an image, it can handle missing information easily. If a state doesn't report data for a week, or if a specific week is missing, the AI can "fill in the gaps" just like it fills in the future.
No "Black Box" Rules: Unlike older models that rely on strict biological rules (which can break if the virus changes), this model learns the "vibe" of flu seasons from data. It captures the messy, complex reality of how diseases spread.

In short: Influpaint is an AI artist that learns to paint flu seasons. By looking at the past few weeks of a current season, it can paint a hundred different versions of what the rest of the season might look like, helping officials prepare for the most likely outcomes.

1. Problem Statement

Forecasting infectious disease incidence is critical for public health planning but remains challenging due to the complex, non-stationary nature of epidemic dynamics. Existing approaches face specific limitations:

Mechanistic models rely heavily on baseline assumptions and often fail to capture realistic emergent dynamics or multimodal uncertainty.
Statistical time-series models excel at historical pattern recognition but are brittle when underlying processes shift (e.g., novel pathogens) and struggle to represent the full spectrum of plausible future trajectories.
Current gaps: There is a lack of methods that can simultaneously capture high-dimensional spatiotemporal structure, diverse epidemic patterns (e.g., bimodal peaks), and robust uncertainty quantification in real-time.

2. Methodology: Influpaint

The authors introduce Influpaint, a generative framework applying Denoising Diffusion Probabilistic Models (DDPMs) to influenza forecasting.

A. Data Representation

Image Analogy: Influenza seasons are encoded as 2D "images" of shape $52 \times L$ (52 weeks $\times$ 51 locations: 50 US states + DC).
Pixel Intensity: Represents the incidence of influenza hospitalizations.
Benefit: This representation allows the direct application of state-of-the-art image generation architectures (U-Nets) to epidemiological data.

B. Training Data Strategy

To overcome data scarcity and heterogeneity, the model is trained on a hybrid dataset:

Surveillance Data: CDC FluView (ILI percentages) and FluSurv-NET (hospitalizations).
Synthetic Data: Trajectories from the Flu Scenario Modeling Hub (SMH) and the flepiMoP model.
Optimal Composition: Ablation studies revealed that a mix of 30% surveillance and 70% simulated trajectories yielded the best performance, outperforming both pure surveillance and pure simulation datasets.

C. Model Architecture & Training

Architecture: A convolutional U-Net with ResNet blocks, group normalization, and self-attention mechanisms.
Diffusion Process:
- Forward: Adds Gaussian noise to the image over $T$ steps (tested $T=200$ and $T=500$ ; 500 performed better).
- Reverse: A neural network predicts and removes noise to reconstruct the image.
- Objective: Minimize the mean squared error between the true noise and the predicted noise ( $L = \mathbb{E}[\|\epsilon - \epsilon_\theta(x_t, t)\|^2]$ ).
Preprocessing: Square-root scaling of incidence values was found to improve performance over linear scaling.

D. Forecasting via Conditional Inpainting

Forecasting is formulated as an inpainting task:

Mechanism: The model is conditioned on partial observations (historical data) and generates the missing future data.
Algorithm: The authors utilize CoPaint (an optimized DDIM sampler). Unlike earlier methods (RePaint) that caused boundary misalignment, CoPaint uses a Bayesian formulation to jointly update revealed and unrevealed pixels at every denoising step.
Features:
- Arbitrary Masks: Supports any spatiotemporal observation pattern (e.g., missing states, missing weeks, checkerboard patterns).
- Ensemble Generation: Produces 512 conditional trajectories to represent the full probabilistic distribution of future outcomes.

3. Key Contributions

First Application of DDPMs to Epidemiology: This is the first study to apply diffusion models to infectious disease forecasting, demonstrating their ability to learn rich, high-dimensional spatiotemporal distributions.
Hybrid Data Framework: Demonstrated that combining limited real-world surveillance with abundant synthetic mechanistic model outputs significantly improves deep learning forecast skill.
Flexible Inpainting: Showed that a single trained model can handle diverse missing data scenarios (spatial gaps, temporal gaps) without retraining, leveraging the generalization properties of diffusion inpainting.
Competitive Real-Time Performance: Validated the approach in the CDC FluSight challenge, achieving top-tier rankings in the 2024–2025 season.

4. Results

A. Unconditional Generation

The model generates realistic, diverse seasonal trajectories, including single peaks, bimodal peaks, and varying peak timings.
It captures spatial synchrony (mean inter-state correlation of 0.455), though slightly lower than observed historical seasons (0.816).

B. Forecasting Performance (FluSight Challenge)

Retrospective Evaluation (2023–2024 & 2024–2025): Influpaint achieved Weighted Interval Scores (WIS) competitive with the CDC FluSight multi-model ensemble.
- 2023–2024: Ranked 5th/32 (WIS 185,441) vs. Ensemble 8th.
- 2024–2025: Ranked 8th/42 (WIS 450,797) vs. Ensemble 20th.
Real-Time Progression:
- 2022–2023: Early implementation (RePaint) ranked 9th/17; suffered from boundary misalignment.
- 2023–2024: Ranked near the bottom (24/27) due to calibration issues.
- 2024–2025: After refining the conditioning algorithm (CoPaint) and dataset, the model ranked 1st in Absolute WIS and MAE among 36 models.
Calibration: While accuracy improved, the model became "overconfident" in 2024–2025 (empirical 50% coverage dropped to 14.8% vs. target 50%), indicating a need for better uncertainty quantification.

C. Ablation Studies

Diffusion Steps: 500 steps outperformed 200.
Scaling: Square-root scaling of incidence was superior to linear scaling.
Augmentation: Data augmentation techniques (Poisson resampling, temporal padding) generally degraded performance, suggesting the model relies on the specific inductive bias of the training data distribution.

5. Significance and Future Directions

Proof of Concept: Influpaint proves that deep generative models can rival traditional mechanistic and statistical ensembles in infectious disease forecasting without explicit epidemiological equations.
Flexibility: The framework offers a unified workflow for national and subnational forecasting and can interpolate missing data in real-time.
Limitations:
- Interpretability: As a "black box" deep learning model, it lacks mechanistic explanations for predictions.
- Data Bias: Performance is bounded by the quality and diversity of the training data (surveillance + simulation).
- Computational Cost: Training and generating ensembles require significant GPU resources and time compared to simpler models.
Future Work: Potential improvements include training directly on the forecasting task (supervised diffusion), integrating auxiliary covariates (climate, mobility), and combining diffusion models with mechanistic models to learn residual processes.

Conclusion: The paper establishes generative diffusion models as a powerful, flexible tool for spatiotemporal epidemic forecasting, capable of capturing complex uncertainty and diverse dynamics that traditional methods often miss.