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Conditional Diffusion Models for Energy-Efficient Driving
Hemanth Neelgund Ramesh, André Snoeck, Chyi-Fu Hong, Shijing Sun
TL;DR
Electric-vehicle fleet routing needs models that represent uncertain energy demand rather than only point predictions. This paper introduces a latent-conditioned diffusion model with a temporal 1D U-Net to generate battery-current trajectories from route context. The proposed E4 model achieves the strongest overall performance among the evaluated diffusion variants, while learned latent conditioning improves generation quality.
Problem
EV battery-current modeling must represent a conditional distribution because real-world energy demand varies with heterogeneous operating context and deterministic point estimates collapse plausible variability.
Method
The framework jointly uses an encoder to map velocity and ambient temperature into a shared latent representation and a temporal 1D U-Net to denoise current trajectories.
Results
E4 achieves the strongest overall performance among the evaluated diffusion variants on Wasserstein distance and MAE, while preserving sharp transient current peaks.
Takeaways & Limitations
The generative formulation supports sampling plausible current profiles for the same trip conditions, providing a foundation for uncertainty-aware fleet planning and downstream SOC and routing analyses.
Takeaways & Limitations
The framework uses telemetry with a narrow set of conditions and fixed interpolated trajectory lengths, so richer route descriptors and physical trip duration are not fully represented.
Abstract
from arXiv · showhide
Electrification of commercial delivery fleets is shifting fleet routing from distance- and time-based optimization toward energy-aware decision-making. Existing sequence models primarily provide deterministic point estimates or limited uncertainty summaries, which do not capture the range of plausible energy-consumption trajectories required for operational decision-making. In this work, we introduce a conditional diffusion framework that generates EV battery-current profiles conditioned on route features such as vehicle velocity and ambient temperature. The model combines a latent conditioning encoder with a temporal 1D U-Net denoising backbone that enables trip-related conditions to be mapped into a shared representation and guides the reverse diffusion process. We evaluate the framework on an open-access commercial EV telemetry dataset containing 12k trips from 9 vehicles. The proposed latent-conditioned diffusion model generates realistic cur- rent trajectories that capture both the dominant temporal envelope and sharp transient events. The model achieves a Wasserstein distance of 0.0029 between generated and measured current distributions below the real vs real reference distance of 0.0085 indicating that generated samples lie within the empirical variability of the test set. We further demonstrate that learned latent conditioning substantially improves performance over direct condition injection, reducing the Wasserstein distance by 89.1% and MAE by 52.8%. This work demonstrates a generative modeling framework for characterizing EV energy consumption under real-world operating conditions, providing an essential foundation for uncertainty-aware fleet planning in large-scale operational settings.
1 INTRODUCTION
Electrification makes energy consumption uncertainty central to commercial EV fleet routing, while existing sequence models provide limited representations of plausible outcomes. The paper proposes a conditional diffusion framework that generates battery-current trajectories from route features using latent conditioning and temporal denoising.
- Motivation: Energy consumption uncertainty has become a primary operational constraint for electric-vehicle routing.Distance and travel time are insufficient proxies for EV operating cost.
- Motivation: Battery-current demand varies across similar trips with road grade, temperature, payload, traffic, vehicle identity, and battery chemistry.Effective modeling therefore needs heterogeneous dynamic and environmental inputs.
- Related work: Existing uncertainty-aware predictors include quantile regression, prediction intervals, Bayesian neural networks, and ensembles, but the paper motivates trajectory generation as a richer alternative.These approaches extend prediction beyond deterministic point estimates by modeling uncertainty summaries or distributional parameters.
- Contribution: The proposed framework generates EV battery-current time series conditioned on velocity and ambient temperature using a latent encoder and temporal 1D U-Net.The encoder maps route features into a shared representation that guides reverse denoising.
- Contribution: The framework is evaluated on approximately 12,000 commercial EV trips from nine vehicles against deterministic and diffusion-based baselines.The stated evaluation compares distributional fidelity across real-world telemetry.
2 METHODS
The method formulates EV battery-current prediction as conditional trajectory generation rather than deterministic point estimation. It encodes trip context into a latent representation that conditions a temporal diffusion U-Net during reverse denoising, then evaluates fidelity with complementary error, spectral, and distributional metrics.
- Problem formulation: The target is the conditional distribution pθ(i0 | c) of battery-current trajectories given trip context, not only a deterministic point estimate.Context may include velocity and static or slowly varying vehicle, route, terrain, payload, and temperature descriptors.
- Diffusion formulation: Conditional diffusion samples multiple plausible current profiles for one trip context by iteratively denoising Gaussian noise.This supports analyses where risk depends on a range of possible current and energy outcomes.
- Model architecture: The model jointly trains a latent-conditioning encoder and temporal 1D U-Net on a single noise-prediction objective.The encoder maps velocity and temperature context into a shared representation for the denoising backbone.
- Model architecture: Separating condition encoding from reverse denoising accommodates velocity’s fast dynamics and ambient temperature’s slowly varying context.The design avoids forcing the denoising backbone to learn both condition representations and diffusion dynamics simultaneously.
- Model architecture: The latent condition is concatenated with the noisy current input at every reverse diffusion step.This fixed-dimensional interface can incorporate additional route and vehicle descriptors without modifying the denoising backbone.
- Denoising backbone: The temporal U-Net uses multi-resolution encoding, decoding, and skip connections to reconstruct trajectories containing slow structure and high-frequency transients.The architecture is motivated by acceleration and regenerative-braking events in EV current profiles.
- Evaluation: Evaluation combines MAE and RMSE, STFT distance, and 1-Wasserstein distance to assess reconstruction, spectral fidelity, and distributional alignment.The experiments also vary latent conditioning, conditioning variables, noise schedules, and U-Net capacity.
3 RESULTS
The proposed E4 conditional diffusion model generates plausible EV battery-current trajectories that capture temporal structure, transient events, and uncertainty spread. It outperforms alternative conditioning and architecture variants, with learned latent conditioning and suitable network design central to performance.
- Generated trajectories follow the dominant current envelope and capture sharp acceleration, deceleration, and regenerative-braking transients.The model produces a spread across independent samples, including meaningful variation at peak amplitudes.
- 0.0029 WD between generated and actual currents is below the 0.0085 real-versus-real reference, placing generated distributions within test-set variability.The comparison uses held-out test trips and measures distributional fidelity.
- The denoising process rapidly reduces across-sample variance, with most variance reduction occurring by approximately t = 250.The dominant current structure forms progressively as Gaussian noise is transformed into the final trajectory.
- E4 achieves the best overall performance, ranking second in MAE behind only the deterministic LSTM while obtaining a significantly better WD score.The comparison includes deterministic and diffusion-based variants.
- The cosine and linear noise schedules perform similarly, whereas increasing U-Net depth degrades performance by over-smoothing trajectories.The shallow E4 variant has MAE comparable to the proposed E4 model.
- Latent conditioning substantially improves over direct condition injection: D0 has approximately two-fold higher MAE and nine-fold higher WD than E4.Both models receive the same conditioning variables, isolating the learned latent-conditioning pathway as the reported difference.
- Removing velocity causes larger errors than removing temperature, while D2 retains much of the overall trajectory structure because velocity remains available.The trajectory comparison is consistent with the quantitative ablation results.
- The learned latent representation is more ordered along a velocity-dependent trend than the comparatively diffuse raw conditioning space.Figure 5 compares raw conditioning c = [v, T] with learned latent condition z = fψ(c).
4 DISCUSSION
The discussion frames EV battery usage as a generative time-series problem, using latent conditioning and diffusion to generate plausible current profiles while identifying scope and deployment limitations.
- Generative modeling captures stochasticity in real-world fleet battery usage that deterministic sequence models collapse into averaged trajectories.
- The architecture encodes multimodal driving context into a shared latent space and injects it with noisy current inputs throughout reverse diffusion.
- Velocity is the dominant conditioning signal, while learned latent conditioning organizes samples more effectively than direct condition injection.
- The framework is constrained by narrow telemetry conditions, fixed-length trajectories, and the absence of closed-loop routing evaluation for operational deployment.
- Future extensions include native variable-length generation, multivariate battery signals, and coupling with downstream optimization algorithms.
5 CONCLUSION
The conclusion presents a latent-conditioned 1D U-Net diffusion model for EV battery-current generation. It reports strong diffusion-model performance and positions the approach as a foundation for energy-aware fleet decision-making.
- The model combines a conditioning encoder for velocity and ambient temperature with a temporal 1D U-Net for reverse-denoising current trajectories.
- The E4 model achieves the strongest overall performance among evaluated diffusion variants on Wasserstein distance and MAE.
- The approach is intended to support route planners evaluating energy outcomes under real-world driving conditions.
- The study provides openly available commercial-fleet EV data and code for preprocessing and diffusion-model training.
DECLARATION OF INTERESTS
The declaration reports no conflicts of interest and discloses the use of LLM tools during writing and coding, with the authors retaining responsibility for the final publication.
- The authors declare no conflict of interest.
- LLM tools assisted writing and Python debugging, after which the authors reviewed and edited the content.