ModFus-DM: Diffusion-Based Modulation Fusion

• ModFus-DM is a diffusion-based framework that fuses features from unsupervised signal denoising to perform automatic modulation classification.
• It employs a two-stage process with generative pretraining followed by a discriminative stage, enhancing robustness against limited labels, variable signal lengths, and distribution shifts.
• The method achieves competitive accuracies on benchmark datasets by leveraging iterative denoising to capture intrinsic modulation structures and counteract fading channels.

Searching arXiv for the exact topic and closely related papers to ground the article. ModFus-DM denotes “modulation-driven feature fusion via diffusion model,” an unsupervised automatic modulation classification framework built around a diffusion generative model for I/Q signals. It is designed for automatic modulation classification under limited labels, variable signal lengths, distribution shifts, and fading channels, and it couples a modulated signal diffusion generation model with a diffusion-aware feature fusion module to obtain robust modulation representations (Tan et al., 3 Aug 2025). In the provided literature, the exact title refers to wireless signal classification, while closely related “ModFus-DM style” descriptions also appear in robust dynamic multi-modal state estimation and multimodal image fusion (Liu, 2021, He et al., 18 Jun 2025, Deng et al., 2024).

1. Definition, scope, and problem setting

ModFus-DM addresses automatic modulation classification, which aims to identify the modulation format of a received radio signal $s[n]$ without prior knowledge of the transmitter’s parameters. The baseband model is

$$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$

where $r[n] = \mathcal{M}(x[n])$ is the modulated baseband signal from information sequence $x[n]$ and modulation map $\mathcal{M}(\cdot)$, $\alpha$ is channel fading, $\tau$ timing offset, $\Delta f$ carrier frequency offset, $T_s$ sampling interval, $\phi$ phase offset, and $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$0 is additive Gaussian noise (Tan et al., 3 Aug 2025).

The framework is motivated by four stated limitations of existing deep-learning AMC methods: dependence on large labeled datasets, fixed-length input assumption, vulnerability to distribution shifts, and poor limited-label performance. The provided account also notes that self-supervised and contrastive AMC methods rely on task-specific proxy tasks and augmentations, and that mismatched augmentations can yield suboptimal features. ModFus-DM therefore positions diffusion models as representation learners rather than only as data generators: iterative denoising captures multi-scale temporal structure, the training objective is label-free, robustness is induced by reconstruction from highly corrupted conditions, and the convolutional U-Net structure can naturally handle different sequence lengths (Tan et al., 3 Aug 2025).

A common misunderstanding is to treat ModFus-DM as a conventional fully supervised classifier. Its defining property is instead a two-stage procedure: an unlabeled generative pretraining stage followed by a small-label discriminative stage. This separation is central to its reported behavior under limited-label and shifted-distribution conditions (Tan et al., 3 Aug 2025).

2. Two-stage architecture and learning pipeline

ModFus-DM is a two-stage, generative-then-discriminative framework. Stage 1 performs unsupervised modulation representation learning with the modulated signal diffusion generation model. Stage 2 freezes that backbone and trains a diffusion-aware feature fusion module plus classifier using only a small number $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$1 of labeled signals per modulation and SNR (Tan et al., 3 Aug 2025).

The end-to-end pipeline is specified as follows. Complex I/Q sequences $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$2 are formatted as $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$3 real-valued arrays. During Stage 1, a forward diffusion process progressively perturbs the signal to obtain $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$4. A 1D U-Net then takes $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$5 and predicts the noise or equivalently reconstructs $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$6, and the network is trained with a diffusion noise prediction loss. After training, a small forward step such as $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$7 is selected, a slightly noised input $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$8 is generated, and intermediate features are collected from U-Net blocks $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$9. These features are pooled and fused by the diffusion-aware feature fusion module to produce a compact feature vector $r[n] = \mathcal{M}(x[n])$0, which is sent to a linear classifier with softmax (Tan et al., 3 Aug 2025).

The training protocol is sequential rather than joint. Stage 1 minimizes the unsupervised diffusion loss on all training samples treated as unlabeled. Stage 2 keeps the diffusion model frozen and minimizes only the classification loss for the fusion module and classifier. The provided description states that there is no joint generative-discriminative loss and that this design avoids overfitting the generative backbone to the small labeled set (Tan et al., 3 Aug 2025).

This suggests that the central inductive bias of ModFus-DM lies in preserving a representation space shaped by denoising, rather than adapting the entire model to the supervised objective. A plausible implication is that the method is meant to retain modulation structure learned from unlabeled data even when the labeled subset is extremely small.

3. Modulated signal diffusion generation model

The modulated signal diffusion generation model is a diffusion generative model specialized for 1D complex baseband signals. Its forward process is a Markov chain that progressively adds Gaussian noise:

$r[n] = \mathcal{M}(x[n])$1

with $r[n] = \mathcal{M}(x[n])$2 the original I/Q signal and $r[n] = \mathcal{M}(x[n])$3 the diffusion coefficient at step $r[n] = \mathcal{M}(x[n])$4. By composition,

$r[n] = \mathcal{M}(x[n])$5

where

$r[n] = \mathcal{M}(x[n])$6

so that

$r[n] = \mathcal{M}(x[n])$7

For large $r[n] = \mathcal{M}(x[n])$8, $r[n] = \mathcal{M}(x[n])$9 approaches isotropic Gaussian noise (Tan et al., 3 Aug 2025).

The reverse model is learned through noise prediction. With a network $x[n]$0 that predicts $x[n]$1, the clean signal estimate is reconstructed as

$x[n]$2

The training objective is the standard diffusion noise prediction loss,

$x[n]$3

The stated training details are $x[n]$4, AdamW, learning rate $x[n]$5, and 2000 epochs (Tan et al., 3 Aug 2025).

Architecturally, the backbone is a 1D U-Net with encoder blocks $x[n]$6, decoder blocks $x[n]$7, skip connections, and time conditioning. Signals are represented as $x[n]$8 inputs, and the convolutional structure is presented as compatible with variable lengths (Tan et al., 3 Aug 2025). The representation claim made in the source is that denoising forces the model to encode constellation structure, symbol sequences and temporal transitions, and channel distortions and how to invert them. The description further states that early decoder blocks, especially $x[n]$9 and $\mathcal{M}(\cdot)$0, contain the richest discriminative representations (Tan et al., 3 Aug 2025).

4. Diffusion-aware feature fusion and classification

The diffusion-aware feature fusion module, DAFFus, is the mechanism that converts generative diffusion features into classification features. After the diffusion model is trained and frozen, a small forward step is selected; ablation shows $\mathcal{M}(\cdot)$1 is best, with accuracy stable for $\mathcal{M}(\cdot)$2 and then dropping as noise dominates (Tan et al., 3 Aug 2025).

For each block $\mathcal{M}(\cdot)$3, the pooled feature is defined as

$\mathcal{M}(\cdot)$4

where $\mathcal{M}(\cdot)$5 pools along the time dimension to length 1. The collection of block features is

$\mathcal{M}(\cdot)$6

DAFFus focuses on decoder blocks $\mathcal{M}(\cdot)$7, which for $\mathcal{M}(\cdot)$8 means $\mathcal{M}(\cdot)$9–$\alpha$0. These are concatenated channel-wise:

$\alpha$1

and then compressed through a linear layer with activation:

$\alpha$2

with embedding dimension $\alpha$3 (Tan et al., 3 Aug 2025).

The classifier is a single-layer softmax model:

$\alpha$4

Stage 2 uses standard cross-entropy,

$\alpha$5

The stated optimization details are Adam, cosine annealing from $\alpha$6 down to $\alpha$7, 50 epochs, and labeled data counts $\alpha$8 per class per SNR (Tan et al., 3 Aug 2025).

The empirical rationale for DAFFus is explicit. Encoder-only fusion, denoted “Fusion down,” performs poorly due to coarse features. Fusion of all blocks is worse than carefully selected fusion because low-quality features degrade the representation. DAFFus outperforms any single block and the naive fusion schemes; on RML2016.10A with $\alpha$9, it beats the best single block $\tau$0 by $\tau$1 and “Fusion down” by $\tau$2 (Tan et al., 3 Aug 2025).

5. Datasets, evaluation protocol, and reported performance

The reported experiments use four datasets. RML2016.10A contains $\tau$3 signals, SNR from $\tau$4 to $\tau$5 dB, training 800 samples per SNR per type, test 200 per SNR per type, and 11 modulations. RML2016.10B contains $\tau$6 signals, SNR from $\tau$7 to $\tau$8 dB, training 4800 per SNR per type, test 1200 per SNR per type, and 10 modulations. RML2018.01A contains $\tau$9 signals, SNR from $\Delta f$0 to $\Delta f$1 dB, training 3276 per SNR per type, test 819 per SNR per type, and 24 modulations. RML2022 contains $\Delta f$2 signals, SNR from $\Delta f$3 to $\Delta f$4 dB, training 1600 per SNR per type, test 400 per SNR per type, and 11 modulations (Tan et al., 3 Aug 2025).

The evaluation protocol includes supervised baselines MCLDNN, CTDNN, PETCGDNN, GE2E, CCNN, and OSMRNet, and self-/semi-supervised baselines TcssAMR, SemiAMC, SSRCNN, and CPC. Limited-label settings use $\Delta f$5 labeled signals per class per SNR, with 10 Monte Carlo splits averaged for each $\Delta f$6 (Tan et al., 3 Aug 2025).

The headline result is that on the 24-modulation RML2018.01A dataset, with only 10 labeled signals per type at SNR $\Delta f$7 dB, ModFus-DM achieves $\Delta f$8 accuracy. The provided comparison at 12 dB further reports the following. On RML2016.10A, CTDNN trained with all labels reaches $\Delta f$9, ModFus-DM with $T_s$0 reaches $T_s$1, ModFus-DM with $T_s$2 reaches $T_s$3, and ModFus-DM with all labels reaches $T_s$4. On RML2016.10B, PETCGDNN trained with all labels reaches $T_s$5, CTDNN reaches $T_s$6, ModFus-DM with $T_s$7 reaches $T_s$8 while using only $T_s$9 labels, and ModFus-DM with all labels reaches $\phi$0. On RML2018.01A, ModFus-DM with $\phi$1 reaches $\phi$2, with $\phi$3 reaches $\phi$4, and with all labels reaches $\phi$5. On RML2022, CTDNN trained with all labels reaches $\phi$6, ModFus-DM with $\phi$7 reaches $\phi$8, and ModFus-DM with all labels reaches $\phi$9 (Tan et al., 3 Aug 2025).

Against self-/semi-supervised baselines, the stated gains are large in very low-label settings. At $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$00, 8 dB, ModFus-DM beats second-best SSRCNN by $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$01 on RML2016.10A, $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$02 on RML2016.10B, and $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$03 on RML2022. At $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$04 and SNR $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$05 dB, accuracy is at least $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$06 on RML2016.10A, at least $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$07 on RML2016.10B, and at least $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$08 on RML2022 (Tan et al., 3 Aug 2025).

These figures support the narrower claim made in the source: with very small labeled subsets, ModFus-DM is competitive with or superior to fully supervised networks trained on all labels, and with full labels it outperforms the listed baselines (Tan et al., 3 Aug 2025).

6. Robustness to distribution shift, variable length, and channel fading

Distribution-shift evaluation includes cross-dataset transfer between RML2016.10A and RML2016.10B. For SNR $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$09 dB and $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$10, the reported average accuracy is $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$11 for A2B and $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$12 for B2A, whereas the competing self-/semi-supervised methods TcssAMR, SemiAMC, SSRCNN, and CPC remain below approximately $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$13 in the same settings (Tan et al., 3 Aug 2025). The provided interpretation is that diffusion-based denoising encourages modeling intrinsic signal structure rather than dataset-specific artifacts or augmentations.

Variable-length recognition is examined in two ways. In the same-dataset experiment on RML2018.01A, the diffusion model is trained on length 1024 and tested on cropped signals of lengths 64–1024 at SNR $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$14 dB. With $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$15, the reported accuracies are $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$16 for 64 samples, $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$17 for 256, $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$18 for 512, $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$19 for 768, and $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$20 for 1024 (Tan et al., 3 Aug 2025). In cross-length and cross-dataset settings, long-to-short transfer at $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$21, 10 dB, yields $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$22 and $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$23, and short-to-long transfer reaches about $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$24–$$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$25 at 24 dB when training on short signals and testing on long RML2018.01A sequences (Tan et al., 3 Aug 2025).

Fading robustness is evaluated on RML2022. Under Rayleigh fading with variance $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$26, and 10 labeled examples per class, accuracy is within $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$27–$$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$28 of the ideal no-fading case at $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$29, and remains above $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$30 even at $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$31. Under Rician fading with $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$32, and $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$33, accuracy is above $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$34 across all $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$35 (Tan et al., 3 Aug 2025).

The source also reports that a moderate diffusion horizon gives the best trade-off between representation richness and computational cost. In the ablation on total diffusion steps $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$36, mean accuracy on RML2016.10A with $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$37 rises from $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$38 at $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$39 to $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$40 at $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$41, $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$42 at $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$43, and $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$44 at $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$45, then saturates or slightly fluctuates at $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$46 (Tan et al., 3 Aug 2025).

7. Limitations, nomenclature, and related “ModFus-DM style” uses

The stated limitations of ModFus-DM are fivefold. First, it only uses raw complex baseband signals; other informative views such as spectrograms, wavelet scalograms, or constellation diagrams are not exploited. Second, diffusion-model training is computationally expensive because it uses a U-Net, $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$47, and 2000 epochs. Third, performance at deep negative SNRs remains challenging. Fourth, the experimental channel models are AWGN, Rayleigh, and Rician fading, while more complex real-world channels may require extended modeling. Fifth, the method focuses on modulation types rather than protocol recognition, symbol-level demodulation, or joint channel estimation and decoding (Tan et al., 3 Aug 2025).

The name itself also requires careful handling. In the provided material, the exact title “ModFus-DM” refers to the AMC framework above (Tan et al., 3 Aug 2025). However, related descriptions in other domains frame different methods as “ModFus-DM style” systems. In robust dynamic multi-modal state estimation, a DMA-based particle filter for unexpected modality failures introduces binary modality “usefulness,” enumerates $$s[n] = \alpha \cdot r[n-\tau] \cdot e^{j(2\pi \Delta f n T_s + \phi)} + w[n]$$48 model hypotheses, and performs Bayesian model averaging over sensor-availability configurations (Liu, 2021). In multimodal medical image fusion, DM-FNet is described as a diffusion-model-based unified framework that uses a diffusion-trained UNet encoder–decoder, multi-timestep noisy inputs, attention-guided multimodal feature fusion, multiscale feature fusion, and a hybrid loss for MRI–CT, MRI–PET, and MRI–SPECT fusion (He et al., 18 Jun 2025). In lightweight multi-modality image fusion, MMDRFuse is presented as a distilled mini-model with dynamic refresh, featuring a two-convolution student with 113 trainable parameters, digestible distillation, a comprehensive loss, and a history-based refresh strategy (Deng et al., 2024).

A plausible implication is that “ModFus-DM” has become a suggestive label for methods that combine modulation or modality-aware fusion with diffusion or dynamic mechanisms, but the exact arXiv title designates the unsupervised AMC system introduced for modulation representation learning (Tan et al., 3 Aug 2025).