mlsanityData to 7 Oct 2026

Syndrome-Flow Consistency Model Achieves One-step Denoising Error Correction Codes

arXiv 2512.01389 ↗First posted 1 Dec 2025cs.LG cs.AIcited by 1

On the map: Diffusion models → Discrete and text diffusion

Abstract (arXiv)

Error Correction Codes (ECC) are fundamental to reliable digital communication, yet designing neural decoders that are both accurate and computationally efficient remains challenging. Recent denoising diffusion decoders achieve state-of-the-art performance, but their iterative sampling limits practicality in low-latency settings. To bridge this gap, consistency models (CMs) offer a potential path to high-fidelity one-step decoding. However, applying CMs to ECC presents a significant challenge: the discrete nature of error correction means the decoding trajectory is highly non-smooth, making it incompatible with a simple continuous timestep parameterization. To address this, we re-parameterize the reverse Probability Flow Ordinary Differential Equation (PF-ODE) by soft-syndrome condition, providing a smooth trajectory of signal corruption. Building on this, we propose the Error Correction Syndrome-Flow Consistency Model (ECCFM), a model-agnostic framework designed specifically for ECC task, ensuring the model learns a smooth trajectory from any noisy signal directly to the original codeword in a single step. Across multiple benchmarks, ECCFM attains lower bit-error-rate (BER) and frame-error-rate (FER) than transformer-based decoders, while delivering inference speeds 30x to 100x faster than iterative denoising diffusion decoders.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Placed in Discrete and text diffusion, one of 14 directions in Diffusion models. Builds on 32 of its 42 references that are in the map. First posted on arXiv 1 Dec 2025.

Builds on

32 of 42 references.

Closest ancestors · 2

Same direction, newest first

  1. 2025Large Language Diffusion Models14 Feb
  2. 2023Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution25 Oct

Other references · 30

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  4. 2020Denoising Diffusion Implicit Modelscited by 9,655
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  6. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  7. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  8. 2023SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesiscited by 4,290
  9. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  10. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  11. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Stepscited by 1,961
  12. 2023Consistency Modelscited by 1,778
18 more
  1. 2023Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Modelscited by 1,465
  2. 2023Improved Techniques for Training Consistency Modelscited by 430
  3. 2022Latent Video Diffusion Models for High-Fidelity Long Video Generationcited by 385
  4. 2023DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimizationcited by 216
  5. 2024Consistency Models Made Easycited by 140
  6. 2022Error Correction Code Transformercited by 47
  7. 2018Communication Algorithms via Deep Learningcited by 42
  8. 2019Hyper-Graph-Network Decoders for Block Codescited by 42
  9. 2018Deep Learning for Decoding of Linear Codes - A Syndrome-Based Approachcited by 34
  10. 2017Neural Offset Min-Sum Decodingcited by 24
  11. 2022Denoising Diffusion Error Correction Codescited by 23
  12. 2024CrossMPT: Cross-attention Message-Passing Transformer for Error Correcting Codescited by 20
  13. 2021Autoregressive Belief Propagation for Decoding Block Codescited by 15
  14. 2023Boosting Learning for LDPC Codes to Improve the Error-Floor Performancecited by 10
  15. 2024Learning Linear Block Error Correction Codescited by 8
  16. 2024Recent Advances in Deep Learning for Channel Coding: A Surveycited by 6
  17. 2025Interplay Between Belief Propagation and Transformer: Differential-Attention Message Passing Transformercited by 5
  18. 2019Learning to Denoise and Decode: A Novel Residual Neural Network Decoder for Polar Codescited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Scalable Mamba-Based Message-Passing Neural Decoder for Error-Correcting Codescited by 0

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