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Conditional Diffusion Models for Energy-Efficient Driving

Hemanth Neelgund Ramesh, André Snoeck, Chyi-Fu Hong, Shijing Sun

arXiv:2608.28142v1cs.LG

TL;DR

EV energy uncertainty is a primary routing constraint, yet deterministic point estimates do not represent the conditional distribution of battery-current trajectories. This paper uses conditional diffusion to generate current profiles from route features, and its E4 model achieves the strongest overall performance among evaluated diffusion variants in Wasserstein distance and MAE.

  • Problem

    EV energy uncertainty is a primary routing constraint, while deterministic point estimates do not represent the conditional distribution of battery-current trajectories.

    Source: §1 · p. 1, PROBLEM FORMULATION · p. 3

  • Method

    A conditional diffusion model generates EV battery-current profiles from route features by encoding them into a shared latent representation that guides reverse denoising.

    Source: §1 · pp. 2–3

  • Results

    The E4 model achieves the strongest overall performance among evaluated diffusion variants in both Wasserstein distance and MAE.

    Source: §5 · p. 9

  • Takeaways & Limitations

    Sampling plausible current profiles for the same trip conditions supports downstream fleet applications such as SoC estimation, battery-health-aware routing, and operational analysis.

    Source: §4 · p. 7

    The framework relies on publicly available passenger-EV telemetry with a narrow set of conditions, primarily velocity and temperature.

    Source: §4 · p. 8

Abstract

from arXiv · show

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

EV fleet routing must account for uncertain energy demand because distance and travel time alone do not ensure trips can be completed within available charge. This work proposes conditional diffusion to generate battery-current trajectories from route features for uncertainty-aware planning.

1 INTRODUCTION

  • Distance and travel time are insufficient proxies for EV operating cost, making energy consumption and available charge central fleet-routing constraints.Electrification of last- and middle-mile delivery fleets is accelerating across major logistics networks.Source: §1 · pp. 1–2
  • EV energy demand varies with road grade, temperature, payload, traffic, vehicle and battery characteristics, and stochastic driving behavior.Effective modeling must integrate heterogeneous route and weather features while capturing variation across operating scenarios.Source: §1 · p. 2
  • Standard regression-trained sequence models predict mean or median demand, suppressing variability needed for route-feasibility assessment; sequence architectures nevertheless outperform distance-based heuristics and static physics models [5].Prior sequence models use driving dynamics, vehicle characteristics, and environmental conditions.Source: §1 · p. 2
  • Existing probabilistic methods estimate uncertainty, but sampling diverse, physically plausible trajectories for a fixed context calls for more flexible conditional generation [18] [20].Diffusion models learn conditional distributions; prior time-series work includes TimeGrad, CSDI [28], and mixed-input conditioning in Time Weaver.Source: §1 · p. 2
  • The proposed framework generates EV battery-current profiles conditioned on velocity and ambient temperature, using a latent encoder to guide reverse denoising in a temporal 1D U-Net.The framework is evaluated on approximately 12,000 trips from nine commercial EVs; the overview depicts route features encoded into a shared representation for denoising.Source: §1 · pp. 2–3, Figure 1 · p. 3

2 METHODS

The methods formulate EV battery-current generation as a conditional distribution problem and use a latent-conditioned diffusion model to generate trajectories from trip context. The study evaluates this approach on commercial-fleet telemetry using architectural variants and reconstruction, spectral, and distributional metrics.

PROBLEM FORMULATION

  • For each trip, the target is a length-L battery-current trajectory, and the model estimates its conditional distribution so multiple plausible profiles can be sampled.Sampling starts from Gaussian noise and iteratively denoises under trip context, supporting downstream SOC and energy-feasibility analyses of variable current and energy outcomes.Source: PROBLEM FORMULATION · p. 3

DATA SOURCES AND PREPROCESSING

  • The dataset contains 11,945 valid trips from nine commercial EVs, with current conditioned on velocity and ambient temperature after interpolation to 512 time steps.Trips were split into training, validation, and test partitions at 70/15/15; the telemetry dataset was compiled by Rücker et al..Source: DATA SOURCES AND PREPROCESSING · p. 3

MODEL ARCHITECTURE

  • The model uses a learned latent encoder for velocity and temperature conditions with a temporal 1D U-Net denoiser, trained jointly to predict noise.The encoder projects and contextualizes the conditioning sequence before compressing it to a latent representation; the U-Net uses multi-resolution paths, skip connections, and dilated residual blocks to capture temporal context and transients.Source: MODEL ARCHITECTURE · pp. 4–5, Figure 2 · p. 4
  • The diffusion model follows a DDPM forward-noising and learned reverse-denoising process, using 1,000 sampling steps and a cosine noise schedule [31] [36].The latent condition is concatenated with the noisy current at each reverse step, and the fixed-dimensional representation allows additional descriptors to be encoded without changing the denoiser.Source: MODEL ARCHITECTURE · pp. 4–5

EXPERIMENTS

  • Experiments compare the latent-conditioned cosine-schedule Model E4 with direct condition injection, condition-variable ablations, alternative noise schedules, U-Net channel depths, and a deterministic LSTM baseline.D0 bypasses the latent encoder; D1 excludes velocity, and D2 excludes ambient temperature.Source: EXPERIMENTS · p. 5

EVALUATION METRICS

  • Evaluation uses MAE and RMSE for pointwise reconstruction, STFT distance for spectral fidelity, and 1-Wasserstein distance for distributional alignment.Source: EVALUATION METRICS · p. 5

3 RESULTS

The results show that the proposed E4 model generates plausible EV current trajectories within measured test-set variability, with performance shaped by its learned conditioning representation, input features, and network capacity.

3 RESULTS

  • E4 follows held-out trip current envelopes, captures sharp acceleration, deceleration, and regenerative-braking transients, and preserves spread across generated samples.Figure 3a shows the spread across 10 generated samples for the same conditioning input, including variability at peak amplitudes.Source: §3 · p. 5, Figure 3 · p. 6
  • Generated-versus-real WD is 0.0029, below the real-versus-real reference of 0.0085, and E4 ranks second in MAE behind the deterministic LSTM.The generated distribution therefore lies within empirical test-set variability; E4 achieves a significantly better WD score than the LSTM-oriented regression comparison.Source: §3 · p. 6, Figure 3 · p. 6, Figure 4 · p. 7
  • Reverse-sampling variance falls rapidly from the initial noise state, with most reduction by approximately t = 250 and later steps mainly refining local fluctuations.The reported diagnostic is the denoising trajectory in Supplementary figure S2.Source: §3 · p. 6
  • E4 with a linear noise schedule performs close to cosine E4, while deeper U-Net capacity degrades performance through over-smoothing; shallow E4 has comparable MAE.The paper attributes cosine E4's slightly better distributional fidelity to smooth signal corruption.Source: §3 · p. 6
  • Direct-conditioning D0 has approximately two-fold higher MAE and nine-fold higher WD than E4; removing velocity increases error substantially, while removing temperature has a smaller effect.Trajectory comparisons also show noticeable deviations for D1 and D2, particularly when velocity is removed; D2 retains much of the overall structure by keeping velocity.Source: §3 · pp. 6–7, Figure 4 · p. 7
  • UMAP shows raw conditioning inputs lack clear velocity organization, whereas learned latent conditions form a velocity-dependent trend that helps explain E4's advantage over D0.The results link this organization to velocity's importance for generating current trajectories and to improved generation from an intermediate latent representation.Source: §3 · p. 7

4 DISCUSSION

The discussion frames EV battery usage as a stochastic time-series task: conditional diffusion generates plausible current profiles for the same trip conditions and may support downstream fleet applications.

Architecture

  • The two-stage architecture encodes multimodal driving context into a shared latent space and concatenates it with noisy current at each reverse diffusion step.The modular encoder can accommodate additional channels such as road grade, payload, fleet identity, or real-time traffic without changing the denoising backbone.Source: §4 · p. 8

Results

  • E4 outperforms the tested diffusion models and significantly improves on LSTM in WD while generating current-trajectory distributions that preserve sharp transient peaks.The model’s distributional generation is presented as an advantage over deterministic point predictions that collapse variability into an averaged trajectory.Source: §4 · pp. 7–8

Conditioning and design findings

  • Velocity is the dominant conditioning signal, latent samples organize by velocity and improve fidelity over direct injection, while noise-schedule choice has minimal influence.The discussion attributes performance more to residual connections and BlurPool layers than to noise schedule, with diminishing returns from increased channel depth.Source: §4 · p. 8

Limitations

  • The study uses passenger-EV telemetry with a narrow range of conditions, generates fixed-length interpolated trajectories, and lacks closed-loop evaluation in active routing and planning.Distributional fidelity alone is insufficient to demonstrate operational deployment value.Source: §4 · p. 8

Future directions

  • Future work could support native variable-length generation via adaptive projection or a DiT backbone, co-generate voltage and current, and couple generated profiles with downstream optimization.The discussion names reinforcement learning as one option for using profiles across sequential segments to reduce aggregate energy consumption and maximize operational feasibility.Source: §4 · pp. 8–9

5 CONCLUSION

The conclusion presents E4 as the strongest evaluated diffusion variant on Wasserstein distance and MAE, while noting LSTM’s slightly lower MAE for deterministic point prediction. It identifies learned latent conditioning and velocity as important to generation quality and points to richer route data and closed-loop planning as future work.

5 CONCLUSION

  • The model combines a conditioning encoder that maps velocity and ambient temperature into a structured latent representation with a temporal 1D U-Net diffusion backbone.Reverse denoising reconstructs realistic battery-current trajectories.Source: §5 · p. 9
  • E4 achieves the strongest overall performance among evaluated diffusion variants in Wasserstein distance and MAE, while LSTM has slightly lower MAE as a deterministic point predictor.The conclusion attributes the LSTM result to its deterministic design and pointwise-prediction objective.Source: §5 · p. 9
  • Ablations show that learned latent conditioning improves generation quality and velocity is the dominant conditioning signal for battery-current profile generation.Source: §5 · p. 9
  • Future work should add richer weather, traffic, and road descriptors, support variable-length trips and multivariate battery signals, and integrate with closed-loop routing or planning systems.The approach is intended to help route planners evaluate energy outcomes under real-world driving conditions.Source: §5 · p. 9

DATA AND CODE AVAILABILITY

  • The commercial-fleet EV dataset is openly available from Rücker et al., and preprocessing and diffusion-model training code is available on GitHub.The passage provides the dataset record and code repository links.Source: DATA AND CODE AVAILABILITY · p. 9

DECLARATION OF INTERESTS

The authors report no conflicts of interest and disclose using LLM tools during writing and Python debugging, while taking responsibility for the final publication.

DECLARATION OF INTERESTS

DECLARATION OF AI-ASSISTED TECHNOLOGIES

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