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One-Step Generative CSI Prediction
Mehdi Sattari, Javad Aliakbari, Alexandre Graell i Amat, Tommy Svensson
TL;DR
CSI prediction must contend with channel aging, while existing deterministic predictions do not directly quantify uncertainty. This paper uses a channel-informed prior in one-step MeanFlow generation; it reports comparable point accuracy to diffusion with better-calibrated predictions and downstream performance.
Problem
CSI prediction faces channel aging, and deterministic predictors provide no direct measure of predictive uncertainty for assessing reliability.
Source: §I · p. 1Method
The paper conditions one-step MeanFlow generation on historical CSI and centers its source distribution on an informative future-channel estimate with Gaussian perturbation.
Source: §I · p. 1, A. MeanFlow Training · p. 2Results
One-step MeanFlow achieves point prediction accuracy comparable to few-step diffusion while providing substantially better-calibrated uncertainty and downstream performance.
Source: §V · p. 6Takeaways & Limitations
Increasing the one-step generator size improves NMSE with only a minor latency increase, favoring added generator capacity over additional diffusion sampling steps within the evaluated setting.
Source: §V · p. 6
Abstract
from arXiv · showhide
Channel state information (CSI) prediction has emerged as a promising approach for mitigating channel aging in wireless communication systems. Recently, generative models have been employed to develop CSI prediction frameworks capable of modeling the uncertainty in future channel realizations. However, the high computational complexity and inference latency of these models remain major obstacles to their practical deployment. To address these challenges, this paper focuses on a class of one-step generative models, namely MeanFlow models, in which inference requires only a single neural function evaluation (NFE), significantly reducing computational cost and latency. To alleviate the difficulty of generating CSI directly from noise, we introduce a channel-informed prior that initializes the generation process from an informative estimate of the future channel rather than pure Gaussian noise. Incorporating this channel-informed prior substantially improves both point prediction accuracy and uncertainty calibration. Furthermore, we compare the proposed MeanFlow-based CSI prediction framework with a recent diffusion-based approach. The results demonstrate that MeanFlow achieves comparable point prediction accuracy while producing better-calibrated CSI predictions with only a single NFE.
I. INTRODUCTION
The introduction motivates uncertainty-aware CSI prediction and presents a channel-informed MeanFlow approach to one-step generation. It also frames future-CSI prediction as estimating the conditional mean from past CSI, a task made difficult by unknown, nonlinear, stochastic channel dynamics.
I. INTRODUCTION
- Deep learning CSI predictors improve accuracy over classical methods, but deterministic approaches provide no direct uncertainty measure and struggle with stochastic, potentially multimodal channel evolution.Classical approaches include Kalman filtering, Prony’s method, and autoregressive models; deep-learning methods are cited as –.Source: §I · p. 1
- The paper adapts MeanFlow to CSI prediction with a channel-informed source distribution centered on a coarse estimate of future CSI.MeanFlow's single-NFE generation is presented as a low-latency alternative to iterative diffusion inference.Source: §I · p. 1
- One-step MeanFlow provides better-calibrated predictive distributions than multi-step diffusion at comparable point accuracy, and its improved calibration yields more accurate achievable-rate prediction.The comparison also evaluates point accuracy with NMSE and uncertainty with PICP and CRPS.Source: §I · pp. 1–2
A. Problem Formulation
- Under mean squared error, the optimal future-CSI predictor is the conditional mean, equivalently the minimum mean squared error predictor.Computing it is generally intractable because the conditional distribution is unknown and channel dynamics are nonlinear and stochastic.Source: A. Problem Formulation · p. 2
B. MeanFlow Models
MeanFlow estimates average transport velocity between a source distribution and target data distribution. Its sampling procedure requires only one network evaluation.
B. MeanFlow Models
- MeanFlow directly estimates average transport velocity between a source distribution and the target data distribution.It is a flow-matching-based generative model [13].Source: B. MeanFlow Models · p. 2
- At inference, MeanFlow generates samples with a single network evaluation rather than multiple numerical integration steps.The training objective follows the original MeanFlow formulation [13].Source: B. MeanFlow Models · p. 2
- During training, MeanFlow interpolates between a data sample and a source sample, while an additional time variable defines the interval over which average velocity is estimated.This average-velocity target differs from learning the instantaneous velocity.Source: B. MeanFlow Models · p. 2
III. ONE-STEP GENERATIVE CSI PREDICTION
The proposed predictor conditions a MeanFlow generator on temporal features extracted from historical CSI. Its training centers the source on an encoder prediction, giving the generator a coarse future estimate plus stochastic variation.
III. ONE-STEP GENERATIVE CSI PREDICTION
- A temporal encoder extracts channel-dynamics features from historical CSI, and a conditioned MeanFlow generator produces future CSI in one network evaluation.The framework adapts MeanFlow, originally proposed for image generation, to conditional CSI prediction.Source: §III · p. 2
A. MeanFlow Training
- The encoder produces latent features z and a deterministic prediction µ; z conditions the generator, while µ supplies the informative source prior.The training objective also optimizes the encoder with an auxiliary MSE loss on µ.Source: A. MeanFlow Training · pp. 2–3
- Instead of a zero-mean Gaussian source, training centers the source on the encoder prediction and adds Gaussian perturbation to retain stochasticity across possible future channels.The source uses stop-gradient on µ; the prior reduces transport distance by providing the predictable component directly to the generator.Source: A. MeanFlow Training · p. 2
- Training feeds the interpolated state and latent conditioning to the generator and uses a Jacobian–vector product with a detached target velocity and adaptive loss weighting.These choices follow the original MeanFlow formulation [13] and are used to improve optimization stability.Source: A. MeanFlow Training · pp. 2–3
B. One-Step AR Inference
At each prediction step, the encoder processes CSI history and the generator estimates average transport velocity in one evaluation. The predicted frame is appended to history for autoregressive prediction through the desired horizon.
B. One-Step AR Inference
- At inference, the temporal encoder extracts conditioning features and a deterministic estimate, then perturbs the informative prior to form a source sample for the generator.MeanFlow avoids iterative denoising or ODE integration and estimates average transport velocity in its single evaluation.Source: B. One-Step AR Inference · p. 3
- The predicted frame is appended to the history and reused as input for the next autoregressive prediction step until the desired horizon is reached.Source: B. One-Step AR Inference · p. 3
- Each predicted CSI frame requires only one MeanFlow generator evaluation, giving the method 1-NFE inference per frame.The paper presents this as substantially lower inference complexity than iterative generative models.Source: B. One-Step AR Inference · p. 3
A. Dataset Setup
The dataset is generated with the 3GPP CDL channel model and split into past and future CSI sequences for prediction.
A. Dataset Setup
- Samples generated with the 3GPP CDL channel model have shape [T × 2 × Nt × Nc], with T = 40 OFDM symbols.The dimensions represent OFDM symbols, real/imaginary parts, transmit antennas, and subcarriers.Source: A. Dataset Setup · p. 3
- Each sample contains 30 past CSI observations and 10 future CSI observations, with X = Hp and Y = Hf.Source: A. Dataset Setup · p. 3
- Samples are standardized to zero mean and unit variance.Source: A. Dataset Setup · p. 3
B. Network Architecture and Training
The architecture uses a shared backbone for diffusion and MeanFlow, while evaluation assesses point accuracy and predictive-distribution quality across prediction steps and horizons.
B. Network Architecture and Training
- Diffusion and MeanFlow share a temporal ConvLSTM encoder and 2D U-Net generator, differing in training objective and sampling procedure.The encoder produces a conditioning latent and point estimate; diffusion uses 3-step DDIM, while MeanFlow samples in one NFE.Source: B. Network Architecture and Training · pp. 3–4
C. Evaluation Metrics
- Evaluation uses 30 generated CSI samples, computes metrics in physical channel space, and bases NMSE on the ensemble mean.Source: C. Evaluation Metrics · p. 4
- PICP measures how often the true value lies within a prediction interval; calibration is indicated by PICP(p) ≈ p.Source: C. Evaluation Metrics · p. 4
- CRPS evaluates predictive-distribution accuracy and sharpness, while achievable-rate CRPS compares generated rate distributions with the true rate.Metrics are reported per prediction step and as horizon averages.Source: C. Evaluation Metrics · p. 4
D. Numerical Results
MeanFlow provides better-calibrated predictions than diffusion while maintaining nearly identical NMSE, and the channel-informed prior improves point accuracy for both generators. Across inference SNRs, µ-MeanFlow balances coverage and achievable-rate CRPS well, while additional DDIM steps improve—but do not eliminate—diffusion’s overconfidence.
D. Numerical Results
- Approximately 5 dB: the informative prior improved average NMSE for both diffusion and MeanFlow, whose prior-based variants achieved nearly identical performance.Centering around µ replaces generating CSI directly from noise with modeling a zero-mean residual.Source: D. Numerical Results · p. 4
- Coverage was 0.73 at nominal 0.90 for MeanFlow, versus 0.18 for overconfident diffusion; MeanFlow also achieved the lowest CRPS with nearly identical NMSE.The calibration advantage persisted with and without the informative prior, suggesting it primarily comes from flow matching.Source: D. Numerical Results · pp. 4–5, Table II · p. 5
- Across inference SNRs, µ-MeanFlow had the closest coverage to nominal and the lowest achievable-rate CRPS at 0–10 dB; at 20 dB, µ-Diffusion’s CRPS was marginally lower (0.16 versus 0.17) but coverage was much lower (0.18 versus 0.72).All models under-covered relative to nominal 0.90, and µ-MeanFlow’s intervals became less reliable as input SNR decreased.Source: Table III · p. 5, D. Numerical Results · p. 5
- At 0–10 dB, MeanFlow with prior achieved the lowest achievable-rate CRPS, outperforming few-step diffusion; at 20 dB, the two generative models were comparable as rate approached saturation.The reported calibration advantage translated into downstream gains where predictive uncertainty was most pronounced.Source: D. Numerical Results · p. 5
- Increasing DDIM steps raised diffusion’s 90% coverage from 0.19 to 0.54 while slightly worsening ensemble NMSE from −11.2 to −10.7 dB; 50-step diffusion still trailed µ-MeanFlow’s 0.72 coverage.More sampling steps alleviate, but do not eliminate, diffusion’s overconfidence.Source: Table IV · p. 5, D. Numerical Results · p. 5
E. Inference Complexity and Latency
MeanFlow reduces per-step inference latency by using one generator evaluation, while diffusion requires multiple evaluations. The measured latency gap is substantial, and increasing the size of the one-step generator improves NMSE with only a minor latency increase.
E. Inference Complexity and Latency
- Both methods have 2.2 M parameters and share the temporal encoder and generator; their inference costs differ by generator evaluations, with MeanFlow using 1 NFE and diffusion at least 3.Per-step cost combines one recurrent encoder step with generator cost multiplied by NFE.Source: E. Inference Complexity and Latency · p. 5
- 6.8 ms: MeanFlow’s prediction-step latency, versus 19.8 ms for diffusion at 3 NFE and up to 324.7 ms at 50 NFE, or 2.9× to 47.5× higher latency for diffusion.The encoder step costs 0.35 ms; the same latency ordering appears in FLOPs.Source: E. Inference Complexity and Latency · p. 5, Table V · p. 6
- At roughly half the latency (8.1 vs. 19.8 ms), the largest MeanFlow model reached lower NMSE (−11.67 dB) than the best diffusion configuration (−11.15 dB).Across generator sizes, MeanFlow’s frontier lies below and to the left of diffusion’s; increasing generator size lowers NMSE along a nearly vertical, low-latency line.Source: Figure 4 · p. 6, E. Inference Complexity and Latency · p. 6
V. CONCLUSION
The paper presents MeanFlow as a one-step generative framework for CSI prediction, using a channel-informed prior to improve point accuracy and uncertainty calibration. It reports comparable accuracy to few-step diffusion, better-calibrated uncertainty and downstream performance, and favorable accuracy–latency scaling; future work will explore channel-shaped priors.
V. CONCLUSION
- The framework uses a channel-informed prior and is evaluated against diffusion models with identical encoder and generator architectures.The evaluation covers both point prediction accuracy and predictive distribution quality.Source: §V · p. 6
- One-step MeanFlow matches few-step diffusion in point prediction accuracy while providing better-calibrated uncertainty and downstream performance.Increasing the one-step generator size improves NMSE with only a minor latency increase.Source: §V · p. 6
- Future work will investigate channel-shaped source priors that exploit structured sparsity in angle–delay-domain wireless residuals.The stated aim is to further improve CSI generation and uncertainty estimation.Source: §V · p. 6