LLM-Driven Multi-Modal Biological Spectrum Analysis via Contribution-Aware Dynamic Fusion and Flow-Based Distillation

1. Introduction

Mass spectrometry (MS) and nuclear magnetic resonance (NMR) spectroscopy stand as the twin pillars of modern analytical biochemistry, providing complementary windows into the molecular composition of biological systems [1]. MS excels at detecting low-abundance analytes with high sensitivity and mass accuracy, while NMR offers unparalleled quantitative reproducibility and structural resolution without sample destruction [2]. The integration of these two modalities has long been recognized as a gold standard for comprehensive metabolomic and proteomic profiling, with applications spanning early cancer detection, drug metabolism studies, and precision medicine [3].

Despite their synergistic potential, the joint analysis of MS and NMR data remains a formidable computational challenge. A single liquid chromatography–mass spectrometry (LC-MS) experiment can generate millions of spectral features, many of which correspond to noise, adducts, or isobaric interferences [4]. NMR spectra, while more reproducible, suffer from peak overlap in crowded spectral regions and require sophisticated deconvolution for accurate quantification [5]. Traditional analysis pipelines rely on sequential steps—peak picking, alignment, statistical testing, and manual annotation—that are time-consuming, error-prone, and difficult to scale to the cohort sizes required for clinical biomarker discovery [6].

The advent of deep learning has begun to transform spectral data analysis. Convolutional and recurrent neural networks have been applied to peak detection and spectral denoising [7], while transformer-based architectures have shown promise for peptide identification from tandem MS data [8]. Deep cross-network architectures that integrate heterogeneous feature representations have also demonstrated scalability in vulnerability analysis tasks [9], and modality-agnostic models have proven effective for brain lesion segmentation across imaging modalities [10]. More recently, large language models (LLMs) pre-trained on scientific text and molecular representations have demonstrated an ability to capture complex biochemical patterns [11]. Multi-modal semantic approaches have achieved low-latency inference for real-time recommendation [12], and semantic-geometric collaborative methods have advanced fine-grained detection in document images [13].

However, existing deep learning approaches for biological spectrum analysis exhibit three critical limitations. First, most methods are designed for a single modality—either MS or NMR—and cannot exploit cross-modal complementarity. Second, current fusion strategies typically employ static concatenation or simple attention mechanisms that fail to account for the varying informativeness of each modality across different samples and spectral regions, unlike contribution-aware dynamic multi-modal balancing approaches that have proven effective in audio-visual speech separation [14]. Third, the computational cost of large spectral models precludes their deployment in clinical settings where real-time inference is essential. While knowledge distillation techniques such as knowledge calibration [15] and flow-based transfer [16] have enabled efficient large model compression in other domains, their application to spectral LLMs remains unexplored.

To address these challenges, we propose SpectraLLM, a unified LLM-driven framework for multi-modal biological spectrum analysis. SpectraLLM introduces four key innovations. (1) A modality-agnostic spectral encoder that projects both MS and NMR spectra into a shared token representation space, enabling cross-modal knowledge transfer through shared transformer layers. (2) A contribution-aware dynamic multi-modal balance mechanism that adaptively adjusts the fusion weights of each modality at every layer and for every sample, ensuring that the most informative spectral features drive downstream predictions. (3) A flow-based knowledge distillation strategy that transfers knowledge from the large SpectraLLM teacher to a compact student model via normalizing flows, achieving near-teacher performance with a 4.3× reduction in inference latency. (4) Parameter-efficient transfer learning via lightweight adapter modules [17,18], enabling rapid adaptation to new biological domains (e.g., metabolomics to proteomics) by updating fewer than 5% of total parameters. The broader landscape of parameter-efficient methods has been benchmarked comprehensively in recent work [17], and multi-task adapter approaches have shown strong transfer capabilities [18]. Moreover, omni diffusion LLMs that unify multi-modal generation and understanding [19] inspire our vision of a single spectral model for diverse biological tasks.

We evaluate SpectraLLM on three large-scale biological spectrum benchmarks: MetaboSpectrum-10K (10,000 paired MS-NMR spectra for biomarker discovery), ProteinSpectra-5K (5,000 tandem MS spectra for peptide identification), and CellNMR-3K (3,000 NMR spectra for cell-type classification). Our experiments demonstrate that SpectraLLM consistently outperforms state-of-the-art methods across all benchmarks, achieving an AUC of 0.947 on MetaboSpectrum-10K (3.2% improvement), a peptide identification accuracy of 94.3% on ProteinSpectra-5K, and a cell-type classification accuracy of 91.7% on CellNMR-3K. The distilled student model retains 96.1% of the teacher’s performance while enabling real-time clinical deployment.

The main contributions of this work are:

• We propose SpectraLLM, the first unified LLM-driven framework that jointly processes MS and NMR spectra through a modality-agnostic encoder with contribution-aware dynamic fusion, enabling effective multi-modal biological spectrum analysis.
• We introduce flow-based knowledge distillation for spectral LLMs, achieving near-teacher performance with significantly reduced computational cost, making large-scale spectral analysis feasible in clinical settings.
• We demonstrate through extensive experiments on three benchmarks that SpectraLLM achieves state-of-the-art performance across diverse biological spectrum analysis tasks, while requiring only 5% trainable parameters for domain adaptation via parameter-efficient transfer learning.

2. Results

2.1. Main Benchmark Comparison

We first evaluate SpectraLLM against state-of-the-art methods on the MetaboSpectrum-10K benchmark for multi-label biomarker identification. As shown in Table 1, SpectraLLM achieves the best performance across all metrics, with an AUC of 0.947, AUPR of 0.923, F1 score of 0.912, Pearson correlation of 0.938, and accuracy of 0.904. These results represent a 3.2% improvement in AUC over the strongest baseline BioSpectraFormer, confirming the advantage of our modality-agnostic encoder with contribution-aware dynamic fusion.

2.2. Cross-Dataset Generalization

To assess generalization, we evaluate all methods on the ProteinSpectra-5K and CellNMR-3K benchmarks. Table 2 and Table 3 show that SpectraLLM consistently outperforms baselines across both datasets. On ProteinSpectra-5K, SpectraLLM achieves 94.3% accuracy for peptide identification, surpassing pNovus by 3.1%. On CellNMR-3K, SpectraLLM attains 91.7% accuracy for cell-type classification with a Pearson correlation of 0.938 for metabolite quantification.

2.3. Ablation Study

We conduct an ablation study to evaluate the contribution of each proposed component. Table 4 shows that removing any single component leads to a measurable performance drop. The contribution-aware dynamic balance is the most critical component, whose removal causes a 2.8% AUC decrease, confirming the importance of adaptive multi-modal fusion.

2.4. Scaling Analysis

We investigate how model performance scales with training data size. Figure 1 shows the AUC on MetaboSpectrum-10K as we vary the training set from 1K to 7K samples. SpectraLLM demonstrates steeper scaling gains compared to baselines, particularly in the low-data regime, suggesting that the shared encoder effectively leverages cross-modal signals for data efficiency.

2.5. Robustness to Noise

Biological spectral data is inherently noisy. We evaluate robustness by adding Gaussian noise at different SNR levels to the test set. Figure 2 shows that SpectraLLM degrades gracefully, maintaining an AUC above 0.90 even at SNR = 5 dB, while baselines drop below 0.85. The dynamic multi-modal balance mechanism automatically shifts weight to the less-corrupted modality, enhancing robustness.

2.6. Cell-Type Transfer

We evaluate cross-cell-type transfer by training on 8 cell types and testing on the held-out 4 cell types. Figure 3 demonstrates that SpectraLLM with PETL adapters achieves the highest transfer accuracy (87.3%), outperforming full fine-tuning (84.1%) and indicating that adapter-based adaptation prevents overfitting to source cell types.

2.7. Distillation Efficiency

We compare flow-based distillation with conventional KL-divergence distillation. Figure 4 shows that our flow-based approach retains 96.1% of teacher performance while achieving 4.3× faster inference, compared to 93.8% retention for KL-based distillation. The normalizing flow provides a tighter distribution alignment, especially for capturing multi-modal spectral representations.

2.8. Multi-Modal Contribution Analysis

We analyze the learned fusion weights ${\alpha }^{\mathrm{MS}}$ and ${\alpha }^{\mathrm{NMR}}$ across different sample categories. Figure 5 shows that for metabolite-rich samples (e.g., serum), MS contributes more weight, while for structural characterization tasks (e.g., tissue extract), NMR receives higher weight, demonstrating that the dynamic balance mechanism learns semantically meaningful fusion strategies.

2.9. Convergence Analysis

We track training convergence in terms of validation AUC over epochs. Figure 6 shows that SpectraLLM converges faster than baselines, reaching 0.90 AUC within 35 epochs compared to 52 epochs for BioSpectraFormer. The flow-based distillation student converges even faster (25 epochs), benefiting from the teacher’s representation space.

2.10. Hyperparameter Sensitivity

We study sensitivity to two key hyperparameters: the adapter bottleneck dimension r and the distillation balancing coefficient ${\beta }_1$. Table 5 shows that $r=64$ provides the best trade-off between adaptation quality and parameter efficiency, while ${\beta }_1=0.3$ yields optimal distillation performance.

2.11. Biological Case Study: Early Cancer Detection

To demonstrate clinical relevance, we conduct a focused case study on early-stage pancreatic cancer detection using a subset of MetaboSpectrum-10K (120 cancer vs. 120 control samples). Figure 7 shows that SpectraLLM achieves an AUC of 0.961 and sensitivity of 0.925 at 90% specificity, substantially outperforming the clinical standard CA 19-9 marker (AUC = 0.784) and the best computational baseline (AUC = 0.923).

2.12. Species Transfer

We further evaluate cross-species transfer by training on human serum spectra and testing on mouse serum spectra from an independent collection. Table 6 shows that SpectraLLM with PETL adapters achieves 85.6% accuracy on the mouse dataset, outperforming zero-shot transfer (71.2%) and confirming the generalizability of learned spectral representations across species.

3. Discussion

We have presented SpectraLLM, a unified framework that bridges large language model capabilities with multi-modal biological spectrum analysis. Our results demonstrate three key findings. First, the modality-agnostic encoder effectively transfers knowledge between MS and NMR modalities, enabling the model to learn shared spectral representations that outperform single-modality approaches. The learned fusion weights reveal a biologically meaningful pattern: MS is prioritized for metabolite-rich samples where sensitivity is critical, while NMR dominates for protein-rich tissue extracts where structural resolution is essential. This adaptive behavior echoes the contribution-aware dynamic balancing mechanisms that have proven effective in audio-visual speech separation [14], where different modalities contribute unequally depending on the acoustic environment.

Second, flow-based knowledge distillation provides a tighter alignment between teacher and student distributions compared to conventional KL-divergence, retaining 96.1% of teacher performance while reducing inference latency by 4.3×—a crucial requirement for clinical deployment. The success of normalizing flows for spectral model compression is consistent with recent advances in flow-based knowledge transfer for efficient large model distillation [16] and knowledge calibration distillation [15]. Additionally, techniques for restoring positional encoding information during distillation, such as LinearARD [20], could further improve student model quality by preserving the spectral positional structure that is critical for peak localization.

Third, parameter-efficient transfer learning via lightweight adapters enables rapid domain adaptation with only 4.5% trainable parameters, facilitating the transfer of spectral models across biological domains and even across species. The broader utility of parameter-efficient methods has been established through comprehensive benchmarks [17] and multi-task adapter architectures [18]. Our results extend these findings to the spectral domain, demonstrating that adapter-based adaptation prevents overfitting to source domains while maintaining high transfer accuracy.

Despite these advances, SpectraLLM has several limitations. The current framework requires paired MS-NMR data for training, which may not always be available in practice; extending to unpaired or partially paired settings is an important future direction. The dynamic balance mechanism does not account for spatial or regional variations within a single spectrum, which could further improve performance—a challenge analogous to fine-grained tampering detection in document images [13]. The biological case study, while promising, is limited to a single cancer type and cohort; multi-center validation with larger and more diverse cohorts is needed before clinical translation. Recent work on chain-of-specificity for enhancing task-specific constraint adherence in LLMs [21] and test-time inference scaling with retrieval-augmented reasoning [22] suggest promising directions for improving spectral LLM reliability. Furthermore, comprehensive video benchmarks for fine-grained retrieval [23] inspire the development of similarly rigorous evaluation protocols for multi-modal spectral analysis. The application of LLMs to large-scale spectrum access and analysis [24] and multi-turn reasoning for edge computing [25] further underscore the growing potential of LLM-driven approaches for scalable, real-time spectral inference in resource-constrained clinical environments. Visual speech enhancement techniques [26] and attention-based speech enhancement [27] also offer insights for improving spectral signal processing within our framework, while advances in medical optical coherence tomography [28] highlight the importance of expanding SpectraLLM to additional imaging modalities.

Future work will explore self-supervised pre-training on large unlabeled spectral corpora, integration of clinical metadata as an additional modality, and deployment of the distilled student model in point-of-care settings for real-time disease screening.

4. Methods

4.1. Data Acquisition and Preprocessing

We collected three benchmark datasets for evaluating SpectraLLM. The MetaboSpectrum-10K dataset comprises 10,000 paired liquid chromatography–mass spectrometry (LC-MS) and proton NMR (¹H-NMR) spectra from human serum samples. Serum samples were collected under standardized protocols, with LC-MS acquired on a Q-Exactive Orbitrap (Thermo Fisher) in both positive and negative ionization modes (resolution 70,000; mass range 70–1,050 $m/z$). ¹H-NMR spectra were recorded on a 600 MHz Bruker Avance III spectrometer using the NOESY-presat pulse sequence for water suppression. A total of 150 metabolite labels were annotated via reference standards and the Human Metabolome Database (HMDB).

The ProteinSpectra-5K dataset contains 5,000 tandem MS (MS/MS) spectra from tryptic digests of human cell lines, acquired on a timsTOF Pro (Bruker) in data-dependent acquisition mode. Ground-truth peptide identifications were obtained by searching against the UniProt human database using MaxQuant with 1% FDR at both peptide and protein levels.

The CellNMR-3K dataset includes 3,000 ¹H-NMR spectra from single-cell extracts across 12 cell types (including HEK293, HepG2, MCF-7, and primary T cells), with metabolite concentration ground truth from spike-in experiments using certified reference materials.

All spectral data underwent standardized preprocessing: LC-MS data were centroided, aligned across samples using retention time correction, and filtered to remove features with >30% missing values. NMR spectra were phased, baseline-corrected, and referenced to TSP at 0.0 ppm. Both modalities were discretized into fixed-length vectors: LC-MS spectra into 4,096-dimensional feature vectors (binned $m/z$–retention time pairs), and NMR spectra into 2,048-dimensional vectors (binned chemical shift values).

4.2. Model Architecture

SpectraLLM comprises three core modules: a modality-agnostic spectral encoder, a contribution-aware dynamic multi-modal fusion layer, and a task-specific prediction head.

Modality-Agnostic Spectral Encoder. Given an input spectral vector $\mathbf{x}\in {\mathbb{R}}^d$ (where d is the discretized spectral dimension), we first partition it into $N=d/p$ non-overlapping patches of length p, where p is the patch size ($p=16$ for MS, $p=8$ for NMR). Each patch is linearly projected into a D-dimensional token embedding:

$$\begin{array}{c}\hfill {\mathbf{z}}_i^{\left(0\right)}={\mathbf{W}}_{\mathrm{proj}}{\mathbf{x}}_{[i·p:(i+1)·p]}+{\mathbf{b}}_{\mathrm{proj}},i=1,\dots ,N\end{array}$$

(1)

where ${\mathbf{W}}_{\mathrm{proj}}\in {\mathbb{R}}^{D\times p}$ and ${\mathbf{b}}_{\mathrm{proj}}\in {\mathbb{R}}^D$ are learnable parameters. We prepend a learnable [CLS] token ${\mathbf{z}}_0^{\left(0\right)}$ and add modality-specific positional encodings:

$$\begin{array}{c}\hfill {\mathbf{e}}_i=\left\{\begin{array}{cc}{\mathbf{W}}_{\mathrm{pos}}^{\mathrm{MS}}{\mathbf{p}}_i\hfill & \mathrm{if}\mathrm{input}\mathrm{modality}\mathrm{is}\mathrm{MS}\hfill \\ {\mathbf{W}}_{\mathrm{pos}}^{\mathrm{NMR}}{\mathbf{p}}_i\hfill & \mathrm{if}\mathrm{input}\mathrm{modality}\mathrm{is}\mathrm{NMR}\hfill \end{array}\right.\end{array}$$

(2)

where ${\mathbf{p}}_i$ is the sinusoidal positional code at position i, and ${\mathbf{W}}_{\mathrm{pos}}^{\mathrm{MS}},{\mathbf{W}}_{\mathrm{pos}}^{\mathrm{NMR}}\in {\mathbb{R}}^{D\times D}$ are modality-specific projection matrices. The token sequence ${\{{\mathbf{z}}_i^{\left(0\right)}+{\mathbf{e}}_i\}}_{i=0}^N$ is then processed by L shared transformer encoder layers with multi-head self-attention (MHSA) and feed-forward networks (FFN):

$$\begin{array}{cc}\hfill {\mathbf{z}}_i^{(\ell +1)}& =\mathrm{MHSA}\left({\mathbf{z}}_i^{(\ell )}\right)+{\mathbf{z}}_i^{(\ell )}\hfill \end{array}$$

(3)

$$\begin{array}{cc}\hfill {\mathbf{z}}_i^{(\ell +1)}& =\mathrm{FFN}\left({\mathbf{z}}_i^{(\ell +1)}\right)+{\mathbf{z}}_i^{(\ell +1)}\hfill \end{array}$$

(4)

The shared encoder enables cross-modal knowledge transfer: representations learned from MS spectra inform NMR interpretation and vice versa.

Contribution-Aware Dynamic Multi-Modal Balance. For paired MS-NMR inputs, we obtain modality-specific [CLS] representations ${\mathbf{h}}^{\mathrm{MS}}={\mathbf{z}}_0^{\left(L\right),\mathrm{MS}}$ and ${\mathbf{h}}^{\mathrm{NMR}}={\mathbf{z}}_0^{\left(L\right),\mathrm{NMR}}$. Rather than static concatenation, we compute adaptive fusion weights at each fusion layer:

$$\begin{array}{cc}\hfill {\alpha }^{\mathrm{MS}}& ={\displaystyle \frac{exp\left({\mathbf{w}}_g^{\top }\sigma ({\mathbf{W}}_g{\mathbf{h}}^{\mathrm{MS}}+{\mathbf{b}}_g)\right)}{{\sum }_{m\in \{\mathrm{MS},\mathrm{NMR}\}}exp\left({\mathbf{w}}_g^{\top }\sigma ({\mathbf{W}}_g{\mathbf{h}}^m+{\mathbf{b}}_g)\right)}}\hfill \end{array}$$

(5)

$$\begin{array}{cc}\hfill {\alpha }^{\mathrm{NMR}}& =1-{\alpha }^{\mathrm{MS}}\hfill \end{array}$$

(6)

where ${\mathbf{W}}_g\in {\mathbb{R}}^{D^{\prime }\times D}$, ${\mathbf{b}}_g\in {\mathbb{R}}^{D^{\prime }}$, ${\mathbf{w}}_g\in {\mathbb{R}}^{D^{\prime }}$ are gating parameters, and $\sigma$ denotes ReLU activation. The fused representation is:

$$\begin{array}{c}\hfill {\mathbf{h}}^{\mathrm{fused}}={\alpha }^{\mathrm{MS}}·{\mathbf{h}}^{\mathrm{MS}}+{\alpha }^{\mathrm{NMR}}·{\mathbf{h}}^{\mathrm{NMR}}\end{array}$$

(7)

This mechanism allows the model to emphasize the more informative modality on a per-sample basis, which is critical when one modality is corrupted by noise or when certain biomarkers are only visible in one spectral domain.

4.3. Flow-Based Knowledge Distillation

To enable clinical deployment, we distill a compact student model (S, 57M parameters) from the large SpectraLLM teacher (T, 350M parameters). We model the teacher-student distribution alignment as a normalizing flow ${\mathbf{f}}_{\theta }$, which provides a flexible and invertible mapping between the student and teacher representation spaces.

Let ${\mathbf{h}}^T\in {\mathbb{R}}^D$ and ${\mathbf{h}}^S\in {\mathbb{R}}^{D_s}$ denote the teacher and student representations, respectively ($D_s<D$). We first project the student representation to match the teacher dimension: ${\tilde{\mathbf{h}}}^S={\mathbf{W}}_p{\mathbf{h}}^S$ where ${\mathbf{W}}_p\in {\mathbb{R}}^{D\times D_s}$. The flow-based distillation loss is:

$$\begin{array}{c}\hfill {\mathcal{L}}_{\mathrm{flow}}=-{\mathbb{E}}_{{\mathbf{h}}^S}\left[log{p}_{{\mathbf{f}}_{\theta }}\left({\tilde{\mathbf{h}}}^S\right)\right]+{\lambda }_{\mathrm{KD}}·\mathrm{KL}\left({\mathbf{f}}_{\theta }\left({\tilde{\mathbf{h}}}^S\right)\parallel {\mathbf{h}}^T\right)\end{array}$$

(8)

where $p_{{\mathbf{f}}_{\theta }}$ is the density induced by the normalizing flow, and ${\lambda }_{\mathrm{KD}}$ is a balancing coefficient. The flow ${\mathbf{f}}_{\theta }$ is implemented as a stack of $K=8$ affine coupling layers, each parameterized as:

$$\begin{array}{cc}\hfill {\mathbf{y}}_{1:d}& ={\mathbf{x}}_{1:d}\odot exp\left(s_{\varphi }\left({\mathbf{x}}_{d+1:D}\right)\right)+t_{\varphi }\left({\mathbf{x}}_{d+1:D}\right)\hfill \end{array}$$

(9)

$$\begin{array}{cc}\hfill {\mathbf{y}}_{d+1:D}& ={\mathbf{x}}_{d+1:D}\hfill \end{array}$$

(10)

where $s_{\varphi }$ and $t_{\varphi }$ are scale and translation networks, and $d=D/2$. The total distillation objective combines flow alignment with task-specific losses:

$$\begin{array}{c}\hfill {\mathcal{L}}_{\mathrm{total}}={\mathcal{L}}_{\mathrm{task}}+{\beta }_1{\mathcal{L}}_{\mathrm{flow}}+{\beta }_2{\mathcal{L}}_{\mathrm{CE}}\end{array}$$

(11)

where ${\mathcal{L}}_{\mathrm{CE}}$ is the cross-entropy between student and teacher soft predictions, and ${\beta }_1,{\beta }_2$ are hyperparameters.

4.4. Parameter-Efficient Transfer Learning

For domain adaptation (e.g., metabolomics → proteomics), we insert lightweight adapter modules into each transformer layer. Each adapter consists of a down-projection, a non-linearity, and an up-projection:

$$\begin{array}{c}\hfill \mathrm{Adapter}\left(\mathbf{z}\right)={\mathbf{W}}_{\mathrm{up}}\sigma \left({\mathbf{W}}_{\mathrm{down}}\mathbf{z}\right)+\mathbf{z}\end{array}$$

(12)

where ${\mathbf{W}}_{\mathrm{down}}\in {\mathbb{R}}^{r\times D}$, ${\mathbf{W}}_{\mathrm{up}}\in {\mathbb{R}}^{D\times r}$, and $r\ll D$ is the bottleneck dimension ($r=64$ in our experiments). During fine-tuning, only the adapter parameters $\{{\mathbf{W}}_{\mathrm{down}},{\mathbf{W}}_{\mathrm{up}}\}$ and the task-specific classification head are updated, while the pre-trained transformer backbone remains frozen. This reduces the number of trainable parameters from 350M to approximately 15.7M (4.5% of total).

4.5. Evaluation Metrics

We evaluate SpectraLLM using the following metrics: AUC (Area Under the ROC Curve) and AUPR (Area Under the Precision-Recall Curve) for biomarker identification; F1 score for multi-label classification; Pearson correlation (r) and Spearman correlation ($\rho$) for metabolite quantification; Accuracy for cell-type classification and peptide identification; and Dice coefficient for spectral region overlap assessment. All metrics are computed on held-out test sets and averaged over five independent runs with different random seeds.

4.6. Implementation Details

SpectraLLM is implemented in PyTorch 2.1 and trained on 8× NVIDIA A100 GPUs (80GB). The teacher model has $L=24$ transformer layers, $D=1024$ hidden dimensions, and 16 attention heads. The student model has $L=12$ layers, $D_s=768$ hidden dimensions, and 12 heads. We use AdamW optimizer with learning rate $1\times {10}^{-4}$, weight decay 0.01, and batch size 32. All models are trained for 100 epochs with cosine annealing learning rate schedule and a 10-epoch warmup. Data augmentation includes random spectral shifting (±0.02 ppm for NMR, ±5 ppm for MS), Gaussian noise injection ($\sigma =0.01$), and random masking of 10% spectral patches. For flow-based distillation, we set ${\lambda }_{\mathrm{KD}}=0.5$, ${\beta }_1=0.3$, ${\beta }_2=0.7$, and use $K=8$ affine coupling layers.