EMFusion: Uncertainty-Aware Conditional Diffusion Model for Multivariate Narrow-band Exposure Forecasting

Hina Tabassum; Jianhua Pei; Luca Chiaraviglio; Yixiang Huang; Zijiang Yan

arxiv: 2512.15067 · v4 · pith:IPZ6RN5Wnew · submitted 2025-12-17 · 💻 cs.LG · cs.AI· cs.SY· eess.SY

EMFusion: Uncertainty-Aware Conditional Diffusion Model for Multivariate Narrow-band Exposure Forecasting

Zijiang Yan , Yixiang Huang , Jianhua Pei , Hina Tabassum , Luca Chiaraviglio This is my paper

Pith reviewed 2026-05-21 17:34 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.SYeess.SY

keywords EMF forecastingdiffusion modelsprobabilistic forecastingwireless networksuncertainty estimationfrequency-selective dataconditional generationnetwork planning

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The pith

EMFusion generates probabilistic EMF forecasts by conditioning a diffusion model on contextual factors like time and season.

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

The paper presents EMFusion as a diffusion-based framework for forecasting electromagnetic field levels at specific frequencies in wireless networks. It learns a conditional distribution over future values to produce full probabilistic intervals rather than single point predictions. A residual U-Net with cross-attention incorporates external conditions while an imputation-based sampling approach treats the task as filling in missing segments to preserve temporal structure. This setup is shown to outperform prior methods on frequency-selective datasets. The approach addresses the need for uncertainty estimates when planning networks and checking compliance.

Core claim

EMFusion is a conditional multivariate diffusion-based probabilistic forecasting framework that integrates diverse contextual factors such as time of day, season, and holidays via a residual U-Net backbone with cross-attention, employs an imputation-based sampling strategy that treats forecasting as a structural inpainting task, and generates empirical probabilistic prediction intervals from the learned conditional distribution rather than point estimates.

What carries the argument

Residual U-Net backbone with cross-attention for dynamic integration of external conditions, paired with imputation-based sampling that frames forecasting as structural inpainting to maintain temporal coherence.

If this is right

EMFusion outperforms baseline models both with and without contextual information on frequency-selective EMF datasets.
It delivers a 23.85 percent improvement in continuous ranked probability score, 13.93 percent in normalized root mean square error, and 22.47 percent reduction in prediction CRPS error.
The model captures inter-operator and inter-frequency variations needed for proactive network planning.
Explicit uncertainty estimates support compliance assessment and health impact evaluation beyond simple point forecasts.

Where Pith is reading between the lines

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

The same conditional diffusion plus inpainting structure could extend to other environmental sensor networks with irregular sampling intervals.
Adding further context such as weather or user density might tighten the probabilistic intervals further.
Real-time deployment could allow networks to adjust transmit power proactively based on forecasted distribution tails.

Load-bearing premise

The imputation-based sampling strategy treats forecasting as a structural inpainting task that ensures temporal coherence even with irregular measurements.

What would settle it

Empirical coverage rates of the generated prediction intervals on held-out frequency-selective EMF data that fall significantly below the nominal probability levels, or no improvement over baselines when contextual factors are removed.

Figures

Figures reproduced from arXiv: 2512.15067 by Hina Tabassum, Jianhua Pei, Luca Chiaraviglio, Yixiang Huang, Zijiang Yan.

**Figure 1.** Figure 1: The U-Net architecture used for EMFusion. The network processes a noisy input through a symmetric encoder-decoder [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

**Figure 2.** Figure 2: EMFusion for multivariate frequency selective EMF forecasting with cross-attention. [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: Comparison of univariate (UV) and multivariate (MV) [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

**Figure 4.** Figure 4: EMF levels in Italian dataset, as a function of network [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

**Figure 5.** Figure 5: Correlation maps of EMF levels for (a) frequency bands, (b) cellular technologies, and (c) network operators. [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗

**Figure 6.** Figure 6: Comparison of EMF Forecasts in Validation Set Across Technology Bands (Top) and Operators (Bottom) [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗

read the original abstract

The rapid growth in wireless infrastructure has increased the need to accurately estimate and forecast electromagnetic field (EMF) levels to ensure ongoing compliance, assess potential health impacts, and support efficient network planning. While existing studies rely on univariate forecasting of wideband aggregate EMF data, multivariate narrow-band EMF forecasting is needed to capture the inter-operator and inter-frequency variations essential for proactive network planning. To this end, this paper introduces EMFusion, a conditional diffusion-based EMF forecasting framework that integrates diverse contextual factors, such as time of day, season, and holidays, while providing uncertainty-aware probabilistic forecasts. The proposed architecture features a residual U-Net backbone enhanced by a cross-attention mechanism that dynamically integrates external conditions to guide the generation process. Furthermore, EMFusion integrates an imputation-based sampling strategy that treats forecasting as a structural inpainting task, ensuring temporal coherence even with irregular measurements. Unlike standard point forecasters, EMFusion generates empirical probabilistic prediction intervals from the learned conditional distribution, providing uncertainty-aware probabilistic forecasting rather than simple point estimation. Numerical experiments conducted on the multivariate narrow-band EMF datasets demonstrate that EMFusion with the contextual information of working hours outperforms the baseline models with or without conditions. The proposed EMFusion outperforms the best baseline by 23.85% in continuous ranked probability score (CRPS) and 13.93% in normalized root mean square error.

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.

Desk Editor's Note private letter to a colleague

EMFusion adapts conditional diffusion models to multivariate frequency-selective EMF forecasting with context and uncertainty, but thin experimental details make the reported gains hard to evaluate.

read the letter

EMFusion is a conditional multivariate diffusion framework for forecasting frequency-selective electromagnetic fields in wireless networks, with built-in uncertainty estimates. It claims to outperform baselines by around 24% in CRPS when using contextual factors like working hours. The new part is the combination of cross-attention in a residual U-Net to handle external conditions and an imputation-based sampling method that turns forecasting into a kind of inpainting problem for better temporal consistency. This moves past the univariate aggregate forecasts that earlier work used. It does a good job of targeting a real application area where probabilistic outputs matter for planning and compliance. The idea of integrating time, season, and holiday data through attention seems practical. The soft spots are in the evaluation. The performance numbers are given without much on the dataset sizes, how baselines were implemented, or checks for statistical significance. That makes it hard to know if the improvements are reliable or tied to specific choices in the experiments. If the full paper has detailed ablation studies or comparisons that show the contribution of each component, that would strengthen it. Right now, it's difficult to separate the effect of the diffusion model from the data handling tricks. This paper would suit readers working on machine learning for wireless systems or environmental data forecasting. Someone looking for diffusion model applications in multivariate time series might get some ideas from the architecture. I would send this for peer review. The approach has promise for the subfield, but the authors will need to expand on the methods and results to make a stronger case.

Referee Report

2 major / 2 minor

Summary. The paper introduces EMFusion, a conditional multivariate diffusion-based probabilistic forecasting framework for frequency-selective EMF levels in wireless networks. It features a residual U-Net backbone enhanced by cross-attention to integrate contextual factors (time of day, season, holidays) and an imputation-based sampling strategy that frames forecasting as structural inpainting to maintain temporal coherence with irregular measurements. Unlike point estimators, it generates empirical probabilistic prediction intervals from the learned conditional distribution. Numerical experiments on frequency-selective EMF datasets report that EMFusion with working-hours context outperforms baselines, achieving a 23.85% improvement in CRPS, 13.93% in normalized RMSE, and 22.47% reduction in prediction CRPS error.

Significance. If the empirical claims hold under rigorous validation, the work offers a meaningful advance in uncertainty-aware forecasting for wireless infrastructure compliance and planning. The shift from univariate wideband aggregates to frequency-selective multivariate probabilistic forecasts, combined with explicit contextual conditioning via cross-attention, addresses practical needs for inter-operator and inter-frequency variation modeling. The diffusion-based approach to generating prediction intervals is a clear strength over deterministic baselines.

major comments (2)

[§4] §4 (Numerical Experiments): The central performance claims (23.85% CRPS improvement, 13.93% NRMSE reduction) are presented without any description of dataset characteristics (number of frequencies, operators, measurement granularity, train/test split ratios, or total samples), baseline definitions (architectures, hyperparameters, or training protocols), or statistical validation (standard errors, confidence intervals, or significance tests). This absence directly undermines evaluation of the superiority claim over baselines with or without conditions.
[§3.2] §3.2 (Imputation-based sampling strategy): The description of the imputation-based sampling as a structural inpainting task that ensures temporal coherence is central to the architecture's ability to handle irregular measurements and integrate cross-attention conditioning. However, no explicit equations, loss formulation, or pseudocode are supplied for the sampling process or its interaction with the residual U-Net, preventing verification that the strategy is not merely heuristic.

minor comments (2)

[Abstract] Abstract: The phrase 'EMFusion with the contextual information of working hours' is ambiguous; it is unclear whether working hours are encoded as a distinct binary or categorical variable separate from the time-of-day embedding, or how this specific context is ablated in the reported results.
[Throughout] Notation throughout: The manuscript uses 'CRPS' without an initial definition or reference to the continuous ranked probability score formula, which may confuse readers unfamiliar with probabilistic forecasting metrics.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment point by point below, indicating the specific revisions we will make to improve the manuscript's rigor and reproducibility.

read point-by-point responses

Referee: [§4] §4 (Numerical Experiments): The central performance claims (23.85% CRPS improvement, 13.93% NRMSE reduction) are presented without any description of dataset characteristics (number of frequencies, operators, measurement granularity, train/test split ratios, or total samples), baseline definitions (architectures, hyperparameters, or training protocols), or statistical validation (standard errors, confidence intervals, or significance tests). This absence directly undermines evaluation of the superiority claim over baselines with or without conditions.

Authors: We agree that the current presentation of the numerical experiments lacks essential details needed to fully evaluate and reproduce the reported improvements. In the revised manuscript, we will expand §4 with a complete description of the frequency-selective EMF dataset, including the number of frequencies, operators, measurement granularity, train/test split ratios, and total samples. We will also specify the baseline architectures, their hyperparameters, and training protocols. Additionally, we will incorporate statistical validation such as standard errors, confidence intervals, and significance tests for the key metrics (e.g., the 23.85% CRPS improvement). These changes will strengthen the evaluation of the claims. revision: yes
Referee: [§3.2] §3.2 (Imputation-based sampling strategy): The description of the imputation-based sampling as a structural inpainting task that ensures temporal coherence is central to the architecture's ability to handle irregular measurements and integrate cross-attention conditioning. However, no explicit equations, loss formulation, or pseudocode are supplied for the sampling process or its interaction with the residual U-Net, preventing verification that the strategy is not merely heuristic.

Authors: We acknowledge that the description of the imputation-based sampling strategy requires greater formality to allow verification. In the revised version, we will augment §3.2 with explicit equations defining the sampling process as a structural inpainting task, the associated loss formulation, and pseudocode detailing its interaction with the residual U-Net backbone and cross-attention conditioning. This will clarify the method as a principled component of the framework. revision: yes

Circularity Check

0 steps flagged

No circularity in the EMFusion derivation or claims

full rationale

The paper presents an empirical ML framework: a conditional diffusion model with residual U-Net backbone, cross-attention for contextual factors, and an imputation-based sampling strategy framed as structural inpainting. All load-bearing claims (probabilistic intervals from the learned conditional distribution, 23.85% CRPS improvement) are supported by numerical experiments on frequency-selective EMF datasets against baselines. No derivation reduces by construction to fitted parameters renamed as predictions, no self-definitional loops in the architecture equations, and no load-bearing self-citations or uniqueness theorems are invoked. The forecasting setup is a standard modeling choice whose outputs are externally validated rather than tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 2 invented entities

Based on abstract only; the framework introduces new architectural components but does not detail numerical free parameters or external benchmarks.

axioms (1)

domain assumption Contextual factors such as time of day, season, and holidays influence EMF levels and can guide the diffusion generation process
Invoked to dynamically integrate external conditions via cross-attention.

invented entities (2)

Imputation-based sampling strategy no independent evidence
purpose: Treat forecasting as structural inpainting to maintain temporal coherence with irregular measurements
New sampling approach introduced to handle missing data in the diffusion process.
Cross-attention enhanced residual U-Net backbone no independent evidence
purpose: Dynamically integrate diverse contextual factors into the conditional generation
Core architectural enhancement proposed for the diffusion model.

pith-pipeline@v0.9.0 · 5802 in / 1378 out tokens · 45826 ms · 2026-05-21T17:34:02.312146+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

EMFusion is based on a CDM for multivariate probabilistic forecasting... residual U-Net backbone enhanced by a cross-attention mechanism... imputation-based sampling strategy that treats forecasting as a structural inpainting task
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

Numerical experiments... outperforms the best baseline by 23.85% in CRPS

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