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Land-then-transport: A Flow Matching-Based Generative Decoder for Wireless Image Transmission

Jingwen Fu, Ming Xiao, Mikael Skoglund, Dong In Kim

TL;DR

This work addresses low-latency wireless image transmission by integrating the wireless channel into a continuous-time generative flow. It introduces Land-then-Transport (LTT), a diffusion-free decoder that uses a Gaussian smoothing flow for AWGN channels and a learned velocity field trained via Conditional Flow Matching, enabling deterministic ODE-based reconstruction starting from a channel-driven landing time $t^{\star}$. The method extends to Rayleigh and MIMO channels by converting observations to AWGN-equivalents with MMSE front-ends, allowing the same flow and velocity field to be reused without retraining. Empirical results on MNIST, Fashion-MNIST, and DIV2K show consistent gains over JPEG2000+LDPC, DeepJSCC, and diffusion-based baselines, with high perceptual quality using as few as 10 ODE steps. Overall, LTT offers a principled, channel-aware, and computation-efficient approach to generative wireless image decoding across diverse channel models.

Abstract

Due to strict rate and reliability demands, wireless image transmission remains difficult for both classical layered designs and joint source-channel coding (JSCC), especially under low latency. Diffusion-based generative decoders can deliver strong perceptual quality by leveraging learned image priors, but iterative stochastic denoising leads to high decoding delay. To enable low-latency decoding, we propose a flow-matching (FM) generative decoder under a new land-then-transport (LTT) paradigm that tightly integrates the physical wireless channel into a continuous-time probability flow. For AWGN channels, we build a Gaussian smoothing path whose noise schedule indexes effective noise levels, and derive a closed-form teacher velocity field along this path. A neural-network student vector field is trained by conditional flow matching, yielding a deterministic, channel-aware ODE decoder with complexity linear in the number of ODE steps. At inference, it only needs an estimate of the effective noise variance to set the ODE starting time. We further show that Rayleigh fading and MIMO channels can be mapped, via linear MMSE equalization and singular-value-domain processing, to AWGN-equivalent channels with calibrated starting times. Therefore, the same probability path and trained velocity field can be reused for Rayleigh and MIMO without retraining. Experiments on MNIST, Fashion-MNIST, and DIV2K over AWGN, Rayleigh, and MIMO demonstrate consistent gains over JPEG2000+LDPC, DeepJSCC, and diffusion-based baselines, while achieving good perceptual quality with only a few ODE steps. Overall, LTT provides a deterministic, physically interpretable, and computation-efficient framework for generative wireless image decoding across diverse channels.

Land-then-transport: A Flow Matching-Based Generative Decoder for Wireless Image Transmission

TL;DR

This work addresses low-latency wireless image transmission by integrating the wireless channel into a continuous-time generative flow. It introduces Land-then-Transport (LTT), a diffusion-free decoder that uses a Gaussian smoothing flow for AWGN channels and a learned velocity field trained via Conditional Flow Matching, enabling deterministic ODE-based reconstruction starting from a channel-driven landing time . The method extends to Rayleigh and MIMO channels by converting observations to AWGN-equivalents with MMSE front-ends, allowing the same flow and velocity field to be reused without retraining. Empirical results on MNIST, Fashion-MNIST, and DIV2K show consistent gains over JPEG2000+LDPC, DeepJSCC, and diffusion-based baselines, with high perceptual quality using as few as 10 ODE steps. Overall, LTT offers a principled, channel-aware, and computation-efficient approach to generative wireless image decoding across diverse channel models.

Abstract

Due to strict rate and reliability demands, wireless image transmission remains difficult for both classical layered designs and joint source-channel coding (JSCC), especially under low latency. Diffusion-based generative decoders can deliver strong perceptual quality by leveraging learned image priors, but iterative stochastic denoising leads to high decoding delay. To enable low-latency decoding, we propose a flow-matching (FM) generative decoder under a new land-then-transport (LTT) paradigm that tightly integrates the physical wireless channel into a continuous-time probability flow. For AWGN channels, we build a Gaussian smoothing path whose noise schedule indexes effective noise levels, and derive a closed-form teacher velocity field along this path. A neural-network student vector field is trained by conditional flow matching, yielding a deterministic, channel-aware ODE decoder with complexity linear in the number of ODE steps. At inference, it only needs an estimate of the effective noise variance to set the ODE starting time. We further show that Rayleigh fading and MIMO channels can be mapped, via linear MMSE equalization and singular-value-domain processing, to AWGN-equivalent channels with calibrated starting times. Therefore, the same probability path and trained velocity field can be reused for Rayleigh and MIMO without retraining. Experiments on MNIST, Fashion-MNIST, and DIV2K over AWGN, Rayleigh, and MIMO demonstrate consistent gains over JPEG2000+LDPC, DeepJSCC, and diffusion-based baselines, while achieving good perceptual quality with only a few ODE steps. Overall, LTT provides a deterministic, physically interpretable, and computation-efficient framework for generative wireless image decoding across diverse channels.
Paper Structure (35 sections, 3 theorems, 76 equations, 5 figures, 6 tables, 2 algorithms)

This paper contains 35 sections, 3 theorems, 76 equations, 5 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Image Transmission in Wireless Systems
  4. Diffusion Models and FM Models
  5. System Model and Problem Formulation
  6. Preliminaries on FM and CFM
  7. LTT: Wireless Transmission as One Step of the Flow Path
  8. Proposed Method in AWGN Channels
  9. AWGN Channel Flow Path
  10. Student Velocity Field Network
  11. Training the Student Velocity Field
  12. Decoding at the Receiver
  13. Scalar Gaussian Benchmark
  14. Complexity--Distortion Trade-off for the ODE Solver
  15. Extension to Rayleigh and MIMO channels
  16. ...and 20 more sections

Key Result

Proposition 1

Consider the scalar Gaussian model above and the ideal probability flow ODE with velocity field $v_t(x) = \frac{\dot s(t)}{s(t)}x$, with the channel output interpreted as the landing point $X_{t^\star}=Y$ where $\sigma(t^\star)=\sigma_{\mathrm{ch}}$. Then the resulting LTT decoder is a linear estima The MMSE linear estimator is and in the high-SNR regime $\sigma_{\mathrm{ch}}^2 \ll \sigma_x^2$, t

Figures (5)

  • Figure 1: Illustration of the proposed land-then-transport scheme: channel outputs land on a Gaussian flow at an effective landing time $t^\star$, and are transported to clean images by a CFM-trained decoder shared across channels.
  • Figure 2: Illustration of FM and CFM. (a) A velocity field transports samples from a simple prior $p_0$ to a target distribution $q$ along continuous trajectories. (b) The induced probability path $(p_t)_{t \in [0,1]}$ smoothly interpolates between $p_0$ and $p_1 = q$. (c) FM trains a neural velocity field $u_t^\theta(X_t)$ to match the true velocity $u_t(X_t)$ along this path. (d) CFM replaces the intractable marginal path with a tractable conditional linear path from $p_0$ to $p_1=q$ by conditioning on $X_1 = x_1$.
  • Figure 3: Training and decoding path in FM and the proposed LTT method.
  • Figure 4: Performance compared to baseline models in AWGN and Rayleigh channels on DIV2K dataset.
  • Figure 5: The visual comparison of reconstructed images on the DIV2K dataset at 20 dB. The first row shows results over AWGN channel, the second row over Rayleigh fading channel, and the third row over MIMO channel. For each channel condition, our method is compared to DeepJSCC and JPEG+LDPC methods.

Theorems & Definitions (3)

  • Proposition 1: High-SNR performance under a scalar Gaussian model
  • Proposition 2: Euler discretization error
  • Proposition 3: Convergence rate of Euler decoding