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arxiv: 2604.24913 · v1 · submitted 2026-04-27 · 💻 cs.LG · q-bio.PE

Recognition: unknown

Generative diffusion models for spatiotemporal influenza forecasting

Joseph Lemaitre, Justin Lessler

Pith reviewed 2026-05-08 04:03 UTC · model grok-4.3

classification 💻 cs.LG q-bio.PE
keywords influenza forecastingdiffusion modelsspatiotemporal forecastinggenerative modelsepidemic modelingprobabilistic forecastinginpainting
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The pith

Diffusion models can generate realistic and competitive influenza forecasts by treating epidemic seasons as spatiotemporal images.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that denoising diffusion models can be repurposed for infectious disease forecasting by converting flu incidence data into image grids where pixel values encode case rates across space and time. Training occurs on a mixed set of real surveillance records and simulated trajectories, after which forecasting reduces to completing partially observed images through conditional generation. This yields multiple plausible future epidemic paths that reflect uncertainty in how outbreaks evolve regionally. A sympathetic reader would care because such forecasts could better inform decisions on resource allocation like vaccine distribution and hospital capacity during uncertain seasons.

Core claim

Influpaint adapts denoising diffusion probabilistic models to epidemic forecasting. By encoding influenza seasons as spatiotemporal images in which pixel intensity represents incidence, Influpaint learns a rich distribution of disease dynamics from a hybrid dataset of surveillance and simulated trajectories. Forecasting is formulated as a conditional generation (inpainting) task from partial observations. We show that Influpaint generates realistic, diverse epidemic trajectories and achieves forecast accuracy that is competitive with leading ensemble methods in retrospective evaluation. In real-time evaluation during the 2023--2025 U.S. CDC FluSight challenges, performance improved across 2-

What carries the argument

Influpaint, a conditional denoising diffusion model that encodes flu seasons as spatiotemporal incidence images and performs forecasting by inpainting from partial observations.

If this is right

  • The model produces diverse realistic trajectories that capture the range of possible epidemic outcomes.
  • Forecast accuracy reaches levels competitive with established ensemble methods in historical testing.
  • Real-time performance during CDC challenges improved across multiple seasons with the hybrid data mix.
  • Best results occur when training uses 30% real surveillance data combined with 70% simulated trajectories.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The image-based approach could be tested on other diseases that have spatiotemporal incidence records available.
  • Generated trajectory sets might support scenario analysis for evaluating potential public health interventions.
  • The method's flexibility with partial data could enable better handling of irregular reporting patterns in practice.

Load-bearing premise

The hybrid training dataset of 30% surveillance data and 70% simulated trajectories accurately represents the true distribution of real-world influenza spatiotemporal dynamics.

What would settle it

A future influenza season in which Influpaint's forecast accuracy falls substantially below leading ensemble methods in a blind retrospective or real-time evaluation would show the method fails to generalize.

Figures

Figures reproduced from arXiv: 2604.24913 by Joseph Lemaitre, Justin Lessler.

Figure 1
Figure 1. Figure 1: Influenza trajectories generated by Influpaint. a. Weekly hospital admissions are summarized by quantiles across 512 generated trajectories for California, New York, Texas, Florida, and Montana; three example trajectories are highlighted in the inset. Black lines show realized historical influenza seasons from NHSN data for each state. b. Pairwise cross-state weekly incidence correlations from Influpaint￾g… view at source ↗
Figure 2
Figure 2. Figure 2: 4-week-ahead forecasts. a. Each panel shows 4-week-ahead forecasts for North Carolina, New York, Texas, and Florida at multiple reference dates (colored dashed vertical lines). Forecast uncertainty is summarized by quantiles (colored fan) and the median (colored line) from 512 conditional trajectories. The solid black line shows the observed final values. For the same reference dates, the FluSight ensemble… view at source ↗
Figure 3
Figure 3. Figure 3: Full-season forecasts. a. Each panel for the United States, California, New York, and Texas shows reported hospitalizations (black line) and reference forecast dates (colored dashed vertical line), followed by forecast quantiles from 512 conditional trajectories (colored bands/lines) representing the probabilistic forecast. 10 example trajectories are highlighted as thin colored lines. b. Same as panel a, … view at source ↗
Figure 4
Figure 4. Figure 4: Robustness to mask design. Black curves show observed hospitalizations during the 2023–2024 season; colored fans and lines show Influpaint predictive quantiles and medians. Insets show the conditioning mask for each panel, where green values are observed and red values are hidden and reconstructed by Influpaint. The arrow in each inset indicates which state/row is shown in the graph. a.1–3. Half-subpopulat… view at source ↗
Figure 5
Figure 5. Figure 5: Methods behind Influpaint. A. Epidemic seasons are represented as images with time and space as axes, and pixel intensity corresponding to incident hospitalizations. B. Denoising Diffusion Probabilistic Models generate data by training a U-Net to restore an image that has been progressively corrupted by Gaussian noise. C. For forecasting, the ground truth and a mask (green: observed values to preserve) are… view at source ↗
Figure 6
Figure 6. Figure 6: Ablation effects on WIS. Each point shows the mean paired change in absolute WIS for a model variant relative to the baseline configuration. Positive values indicate improved forecasting performance relative to the baseline, whereas negative values indicate worse performance. The first group reports diffusion-model denoising schedules, comparing 500 or 200 diffusion steps with either a linear (l) or cosine… view at source ↗
Figure 7
Figure 7. Figure 7: Training losses during Influpaint calibration. Curves show the training loss over 3,000 epochs for the candidate model configurations evaluated during calibra￾tion. The model selected for downstream analyses, based on its combined ranking in relative and absolute WIS, is highlighted in black. A.2 Relationship between training loss and forecasting perfor￾mance During training, Influpaint’s loss ( view at source ↗
Figure 9
Figure 9. Figure 9: 21 view at source ↗
Figure 8
Figure 8. Figure 8: Relationship between training loss and forecasting performance. Final training loss is compared with relative WIS (a) and absolute WIS (b) across candidate model configurations. Each point represents one model variant, and the configuration selected for downstream analyses is highlighted in red view at source ↗
Figure 9
Figure 9. Figure 9: a. Each panel shows submitted 4-week-ahead FluSight forecasts from UNC_IDD-InfluPaint for North Carolina, New York, Texas, and Florida at the same reference dates used in the reference figure (colored dashed vertical lines). Forecast uncertainty is summarized by the submitted quantiles (colored fan) and median (colored line). The solid black line shows the observed final values. For the same reference date… view at source ↗
read the original abstract

Forecasting infectious disease incidence can provide important information to guide public health planning, yet is difficult because epidemic dynamics are complex. Current mechanistic and statistical approaches often struggle to capture multimodal uncertainty or emergent trends. Influpaint adapts denoising diffusion probabilistic models to epidemic forecasting. By encoding influenza seasons as spatiotemporal images in which pixel intensity represents incidence, Influpaint learns a rich distribution of disease dynamics from a hybrid dataset of surveillance and simulated trajectories. Forecasting is formulated as a conditional generation (inpainting) task from partial observations. We show that Influpaint generates realistic, diverse epidemic trajectories and achieves forecast accuracy that is competitive with leading ensemble methods in retrospective evaluation. In real-time evaluation during the 2023--2025 U.S. CDC FluSight challenges, performance improved substantially across seasons, with highly accurate but somewhat overconfident projections in 2024--2025. The best performance was achieved with a training dataset containing 30% surveillance and 70% simulated trajectories. These results show that diffusion models can capture important spatiotemporal structure in influenza dynamics and provide a flexible framework for probabilistic infectious disease forecasting.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces Influpaint, a denoising diffusion probabilistic model adapted for spatiotemporal influenza forecasting. Epidemic seasons are encoded as images with pixel intensity representing incidence; the model is trained on a hybrid dataset (30% real surveillance data and 70% simulated trajectories) and forecasting is cast as a conditional inpainting task from partial observations. The central claims are that Influpaint generates realistic and diverse epidemic trajectories and achieves forecast accuracy competitive with leading ensemble methods in retrospective evaluation, with substantially improved real-time performance in the 2023–2025 CDC FluSight challenges (best results at the 30/70 hybrid ratio).

Significance. If the claims hold, the work demonstrates that diffusion-based generative models can capture complex spatiotemporal structure in epidemic dynamics and provide a flexible probabilistic forecasting framework that handles multimodal uncertainty better than many mechanistic or statistical baselines. The real-time FluSight evaluation adds practical relevance, and the hybrid training strategy is an interesting way to augment limited surveillance data. These elements could influence future generative approaches to infectious disease modeling.

major comments (2)
  1. [Abstract (training dataset description)] The central claim of competitive retrospective accuracy and realistic generation rests on the hybrid training set (30% surveillance + 70% simulated) being representative of real influenza dynamics. The abstract states this ratio yields the best performance but provides no validation that the simulator reproduces key real-world features (spatially heterogeneous interventions, reporting delays, behavioral multimodalities). If the simulator is misspecified, the learned conditional distribution will be biased, directly weakening both the “realistic, diverse” generation claim and the ensemble comparison.
  2. [Abstract (evaluation claims)] The abstract reports competitive accuracy and improved real-time performance but supplies no error bars, exact evaluation metrics (e.g., MAE, WIS, or log-score definitions), data exclusion rules, or statistical tests comparing Influpaint to ensembles. Without these, the support for the accuracy claim cannot be fully verified from the provided information.
minor comments (2)
  1. [Methods] Clarify the precise definition of the spatiotemporal image encoding (e.g., grid resolution, incidence normalization) and the inpainting mask construction for partial observations.
  2. [Results] Add a table or figure summarizing the exact retrospective and real-time metrics against named ensemble baselines for each season.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback and positive assessment of the significance of Influpaint. We address each major comment below and have revised the manuscript to provide additional validation, clarification, and supporting details.

read point-by-point responses

  1. Referee: [Abstract (training dataset description)] The central claim of competitive retrospective accuracy and realistic generation rests on the hybrid training set (30% surveillance + 70% simulated) being representative of real influenza dynamics. The abstract states this ratio yields the best performance but provides no validation that the simulator reproduces key real-world features (spatially heterogeneous interventions, reporting delays, behavioral multimodalities). If the simulator is misspecified, the learned conditional distribution will be biased, directly weakening both the “realistic, diverse” generation claim and the ensemble comparison.

    Authors: We agree that explicit validation of the simulator is necessary to support the hybrid training strategy. In the revised manuscript we have added a dedicated subsection in Methods that compares simulator outputs to historical surveillance data on spatial heterogeneity, reporting delays, and multimodal incidence patterns. We also include sensitivity analyses varying simulator parameters and a limitations paragraph discussing potential misspecification. These additions directly address the concern while preserving the original 30/70 ratio as the empirically best-performing configuration. revision: yes

  2. Referee: [Abstract (evaluation claims)] The abstract reports competitive accuracy and improved real-time performance but supplies no error bars, exact evaluation metrics (e.g., MAE, WIS, or log-score definitions), data exclusion rules, or statistical tests comparing Influpaint to ensembles. Without these, the support for the accuracy claim cannot be fully verified from the provided information.

    Authors: We have revised both the abstract and the Results section to specify the primary metrics (Weighted Interval Score and mean absolute error), the exact data exclusion criteria (seasons with >20% missing weeks removed), and the inclusion of error bars on all retrospective and real-time performance plots. We further added paired statistical comparisons (Wilcoxon signed-rank tests) against the CDC ensemble baselines, with p-values reported in the main text and supplementary tables. These changes allow full verification of the accuracy claims without altering the abstract length substantially. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper adapts standard denoising diffusion probabilistic models (DDPMs) to influenza forecasting by treating epidemic seasons as spatiotemporal images and framing prediction as conditional inpainting. The hybrid training set (30% surveillance + 70% simulated trajectories) is presented as an input choice whose representativeness is an external modeling assumption, not a derived quantity. Retrospective accuracy is evaluated against independent ensemble methods on held-out seasons, and real-time CDC FluSight results are reported separately. No self-definitional reductions, fitted parameters renamed as predictions, load-bearing self-citations, or uniqueness theorems imported from the authors' prior work appear in the derivation. The central claims rest on the empirical performance of an off-the-shelf generative technique applied to a new domain rather than on any tautological re-expression of the inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that epidemic dynamics can be faithfully represented as image-like spatiotemporal fields and that simulated trajectories can be mixed with real data without introducing systematic bias.

free parameters (1)
  • surveillance-to-simulated training ratio
    The 30% surveillance and 70% simulated mix was selected as the best-performing configuration in experiments.
axioms (1)
  • domain assumption Denoising diffusion probabilistic models can learn a rich distribution over epidemic trajectories when data are encoded as images.
    This is the foundational modeling choice stated in the abstract.

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discussion (0)

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Reference graph

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