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arxiv: 2606.05239 · v1 · pith:VB4D7IXFnew · submitted 2026-06-03 · 📊 stat.ML · cs.LG

HyFAD: Hybrid Time-Frequency Diffusion with Frequency-Aware Embedding for Time Series Imputation

Hongfan Gao , Wangmeng Shen , Bin Yang , Jilin Hu This is my paper

Pith reviewed 2026-06-28 04:26 UTC · model grok-4.3

classification 📊 stat.ML cs.LG
keywords time series imputationdiffusion modelshybrid time-frequencyfrequency-aware embeddingDDPMcoarse-to-fine generationspectral guidance
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The pith

HyFAD performs time series imputation using a hybrid diffusion process that moves sequentially from the time domain to the frequency domain with frequency-aware embeddings.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces HyFAD to address limitations in existing diffusion models for time series imputation, specifically their struggles with frequency-sensitive denoising and balancing global trends with local dynamics. It proposes a coupled time-frequency diffusion framework built on DDPM where the reverse process first captures low-frequency trends in the time domain before refining high-frequency components in the frequency domain. A frequency-aware step embedding is added to provide guidance based on the relationship between diffusion steps and spectral components. This setup enables coarse-to-fine generation that leads to state-of-the-art performance on multiple benchmark datasets for imputation tasks.

Core claim

HyFAD adopts a coupled time-frequency diffusion framework in which the reverse denoising proceeds sequentially from the time domain to the frequency domain, enabling coarse-to-fine generation. The time-domain diffusion process captures low-frequency global trends, while the frequency-domain diffusion process refines high-frequency spectral components. A frequency-aware step embedding exploits the relationship between diffusion steps and spectral components to provide step-dependent spectral guidance for more accurate band-wise reconstruction.

What carries the argument

The coupled time-frequency diffusion framework with sequential reverse denoising from time to frequency domain and frequency-aware step embedding that links diffusion steps to spectral components.

If this is right

  • The time-domain stage effectively models global low-frequency trends in the data.
  • The frequency-domain stage allows precise refinement of high-frequency local dynamics.
  • The frequency-aware embedding improves reconstruction accuracy across different frequency bands.
  • Overall, the approach yields superior imputation results compared to prior diffusion methods on benchmarks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This sequential domain switching might apply to other signal types like audio or images where frequency content matters.
  • Future work could explore non-sequential or parallel time-frequency diffusion variants.
  • The frequency-aware embedding could be adapted to other step-conditioned generative models.

Load-bearing premise

That applying diffusion denoising first in the time domain and then in the frequency domain will consistently produce better coarse-to-fine imputation than single-domain approaches.

What would settle it

Experimental results on the benchmark datasets where HyFAD fails to show improved imputation metrics over existing methods that use only time-domain or only frequency-domain diffusion.

Figures

Figures reproduced from arXiv: 2606.05239 by Bin Yang, Hongfan Gao, Jilin Hu, Wangmeng Shen.

Figure 1
Figure 1. Figure 1: An imputation example from Channel 4 on PhysioNet. While CSDI captures coarse trends, [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Noise injection and denoising process in HyFAD. At each forward step, frequency-domain [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Architecture details of our denoising model [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Visualization of imputation results on AQI dataset from Channel 1 to Channel 36. The solid [PITH_FULL_IMAGE:figures/full_fig_p022_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Visualization of imputation results on PhysioNet dataset from Channel 1 to Channel 35 [PITH_FULL_IMAGE:figures/full_fig_p023_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Visualization of imputation results on PhysioNet dataset from Channel 1 to Channel 35 [PITH_FULL_IMAGE:figures/full_fig_p024_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Visualization of imputation results on PhysioNet dataset from Channel 1 to Channel 35 [PITH_FULL_IMAGE:figures/full_fig_p025_7.png] view at source ↗
read the original abstract

Diffusion models have demonstrated strong performance in time series modeling due to their ability to progressively capture complex data distributions through iterative denoising. However, existing approaches struggle with frequency-sensitive denoising, high-frequency reconstruction and balancing global trends with local dynamics. To address these limitations, we propose \textbf{HyFAD}, a \textbf{Hy}brid time-frequency \textbf{D}iffusion model with \textbf{F}requency-\textbf{A}ware embedding for time series imputation. Built upon the DDPM paradigm, HyFAD adopts a coupled time-frequency diffusion framework, in which the reverse denoising proceeds sequentially from the time domain to the frequency domain, enabling coarse-to-fine generation. Specifically, the time-domain diffusion process captures low-frequency global trends, while the frequency-domain diffusion process refines high-frequency spectral components. We further introduce a frequency-aware step embedding that exploits the relationship between diffusion steps and spectral components, providing step-dependent spectral guidance and facilitates more accurate band-wise reconstruction. Extensive experiments on multiple benchmark datasets demonstrate that HyFAD achieves state-of-the-art performance. Our source code is available at https://github.com/hongfangao/HyFAD.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper claims to introduce HyFAD, a hybrid time-frequency diffusion model with frequency-aware embedding for time series imputation. It extends DDPM by using a sequential reverse process starting in the time domain for low-frequency global trends and then moving to the frequency domain for high-frequency spectral components, along with a frequency-aware step embedding for spectral guidance. Extensive experiments on benchmark datasets are said to show state-of-the-art performance.

Significance. If the results hold and the mechanism is validated, the approach could improve diffusion-based time series imputation by better balancing global trends and local dynamics through explicit frequency handling. The open-source code is a strength that allows verification and extension of the work.

major comments (1)
  1. [Experiments] The central claim that the coupled time-frequency reverse process reliably produces coarse-to-fine generation overcoming frequency-sensitive denoising limitations of prior models requires validation through ablations. No such studies isolating the sequential structure (e.g., time-domain diffusion with frequency-aware embedding vs. the full HyFAD) are described, making it difficult to attribute SOTA gains specifically to the proposed mechanism rather than increased model capacity or other factors.
minor comments (1)
  1. [Abstract] Consider adding specific dataset names and performance metrics to the abstract to better convey the experimental scope.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the major comment point by point below.

read point-by-point responses

  1. Referee: The central claim that the coupled time-frequency reverse process reliably produces coarse-to-fine generation overcoming frequency-sensitive denoising limitations of prior models requires validation through ablations. No such studies isolating the sequential structure (e.g., time-domain diffusion with frequency-aware embedding vs. the full HyFAD) are described, making it difficult to attribute SOTA gains specifically to the proposed mechanism rather than increased model capacity or other factors.

    Authors: We agree that the current manuscript lacks explicit ablation studies isolating the sequential time-to-frequency reverse process (e.g., time-domain diffusion with frequency-aware embedding versus the full HyFAD). Such studies would strengthen attribution of gains to the hybrid mechanism rather than capacity or other factors. In the revised manuscript we will add these ablations on the benchmark datasets, including direct comparisons of the time-domain stage alone, frequency-domain stage alone, and the coupled HyFAD model, to validate the coarse-to-fine generation benefit. revision: yes

Circularity Check

0 steps flagged

No circularity: method is an empirical extension of DDPM with no equations, fitted predictions, or self-citation chains in the provided text.

full rationale

The abstract presents HyFAD as a practical architectural extension of the standard DDPM paradigm, with a sequential time-then-frequency reverse process and a frequency-aware embedding introduced by design choice rather than derived from prior results. No equations, parameter-fitting steps, or predictions are described that could reduce to inputs by construction. No self-citations or uniqueness theorems are invoked. The central claims rest on experimental benchmarks, which are external to any internal derivation and therefore not circular. This is the expected outcome for a methods paper whose contribution is a new model architecture rather than a mathematical reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no equations, methods section, or experimental details exist from which to extract free parameters, axioms, or invented entities.

pith-pipeline@v0.9.1-grok · 5743 in / 995 out tokens · 28827 ms · 2026-06-28T04:26:56.899334+00:00 · methodology

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Reference graph

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    + √ λ q βt 1ϵt 1 = q ¯αt 1 ¯αf 1xt 0 + √ 1−λ 1X s=1 q βf 1 s ¯αt 1 ¯αt 0 s ¯αf 1 ¯αf 1 F −1(Λϵt

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    A.3 Details in the reverse process Noise prior in the reverse process.At the end of the forward process, ¯αt k,¯αf k →0 , therefore, the mean of xt k is 0

    is still gaussian with the standard deviation of the sum of two the two groups of gaussian noise. A.3 Details in the reverse process Noise prior in the reverse process.At the end of the forward process, ¯αt k,¯αf k →0 , therefore, the mean of xt k is 0. For the standard deviation term, it is the linear combination of two independent gaussian noises, so th...

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    in Eq.19 is implemented via one-dimensional linear interpolation along the frequency axis using torch.nn.functional.interpolate (mode=’linear’), which resamples the frequency-wise gating vector from ⌊L/2⌋+ 1 frequency bins to d 2 embedding dimensions. The frequency grid fd = [f1, f2,· · ·, f d 2 ]∈R d 2 in Eq.20 is constructed by uniform sampling from [0,...