Audio Super-Resolution with Latent Bridge Models

We thank the reviewer for the valuable and inspiring comments.

Main Comments:

W1 and Q1: If models & code will be publicly available

We appreciate the reviewer's emphasis on reproducibility, which we also consider highly important. We will make our best efforts to release more implementation details and resources to support further research in the audio community, e.g., opening the inference implementation in the first step.

W2: Lacking details on the high-res VAE

We agree that the high-resolution VAE plays a crucial role in our framework.

In fact, we have provided extensive details in Appendix, and we evaluate both the reconstruction and corresponding generation performance of our VAE by training for 200K steps on each configuration. We train each ablated VAE configuration on our full speech corpus (details in Appendix G) for 200K steps, and pair it with a corresponding Latent Bridge Model (LBM) trained for 150K steps. All evaluations are conducted on the VCTK-test set. We kindly refer the reviewer to the following sections for more specifics:

• In Appendix B.1, we outline the VAE architecture and loss formulation, which closely follow the training structure of Stable-Audio-Open [1] and ETTA [2]. Specifically, we adopt a Oobleck[3]-based compression network with DAC[4]-based discriminator.
• In Appendix B.1.1, we conduct a systematic study of compression ratios for super-resolution, ultimately selecting a 512× compression from waveform $\mathbf{x} \in \mathbb{R}^L$ to latent $\mathbf{z} \in \mathbb{R}^{L/512 \times 64}$, and we find that a time-axis compression rate of 512 achieves the best trade-off between efficiency and performance.
• Appendix B.1.2 investigates the effect of KL divergence weight, and includes both quantitative analysis and interpretability discussion. We apply a fixed scaling factor s introduced in Section 3.2, line 166 as 0.25 and KL divergence as 0 (where our VAE degrades into an AutoEncoder).
• Appendix B.1.3 compares our VAE reconstruction quality against recent open-source baselines on 48 kHz audio.
• Appendix B.2 details the training procedures for high-resolution VAE models at 96 kHz and 192 kHz, including parameter choices and convergence behavior.

96Audio dataset

192Audio dataset

For the 96 kHz and 192 kHz VAEs, as shown in Appendix B.2, we adopt the same network architecture and training procedure as the 48 kHz VAE. Moreover, the higher-resolution VAEs are fine-tuned from the lower-resolution ones to alleviate the scarcity of ultra high-resolution training data. We will make this clearer in the final version.

W3: Sampling time can be stated explicitly

The inference efficiency is indeed a key factor for the deployment of high-resolution audio generation models.

To address this, we present below the real-time factor (RTF) and number of function evaluations (NFE) of our method and several representative baselines on a single NVIDIA-A800, all evaluated under the 48 kHz setting:

While our method may not match the inference speed of GAN-based models like [8] and [9], it offers a substantial speedup over other iterative-based models, including Bridge-SR [5], UDM+ [6], and previous SoTA AudioSR [7] (RTF 0.369 vs. 0.948).

When scaling the sampling target to higher sampling rates (e.g., 192 kHz), it naturally leads to slower inference speeds beacuse of the cascade paradigm. Especially, we mitigate the impact by adopting a lighter network architecture, as shown in Appendix G.2, so the inference speed does not increase linearly. As shown, even upsampling to 192 kHz, it is even faster than the 48 kHz waveform-domain bridge system [5] (RTF 1.351 vs. 1.670).

We hope our reply can address your concerns!

[1] Stable Audio Open. ICASSP, 2025

[2] ETTA: Elucidating the Design Space of Text-to-Audio Models. ICML, 2025

[3] Long-form music generation with latent diffusion. ISMIR, 2024

[4] High-fidelity audio compression with improved rvqgan. NeurIPS, 2023

[5] Bridge-SR: Schrödinger bridge for efficient sr. ICASSP, 2025

[6] Conditioning and sampling in variational diffusion models for speech super-resolution. ICASSP, 2023

[7] AudioSR: Versatile audio super-resolution at scale. ICASSP, 2024

[8] Audio super-resolution with robust speech representation learning of masked autoencoder. TASLP, 2024

[9] Neural vocoder is all you need for speech super-resolution. Interspeech, 2022

We thank the reviewer for the valuable comments. We provide a point-to-point response as follows.

Main Comments:

W1: little scientific insight into why the latent-bridge approach yields more informative priors than diffusion or GAN alternatives

Thank you for pointing this out. We respectfully clarify the scientific motivation behind using the latent-bridge approach, which fundamentally lies in how it redefines the prior distribution of the generative process in a way that is more SR task-aligned and informative than the standard Gaussian prior used in conventional diffusion models.

In diffusion models, the trajectory is defined as $\mathbf{z}_ {t,diff} = \alpha(t) \cdot \mathbf{z}_ 0 + \beta(t) \cdot \boldsymbol{\epsilon}, \boldsymbol{\epsilon} \sim \mathcal{N}(0, \mathbf{I}),$ although the LR input is injected as a condition, the generative process itself starts from an uninformative noise prior (typically $\mathbf{z}_T \sim \mathcal{N}(0, \mathbf{I})$). This noise-to-data generation imposes a heavy burden on the model: it must learn to reconstruct the HR target solely from random noise, while separately relying on the condition for guidance. As a result, the prior distribution is misaligned with the actual LR-to-HR task, leading to inefficiency and potential degradation in performance.

In contrast, our latent-bridge model formulate: $\mathbf{z}_ {t,bridge} = \frac{\alpha_ t \bar{\sigma}_ t^2}{\sigma_ 1^2} \, \mathbf{z}_ 0+ \frac{\bar{\alpha}_ t \, \sigma_ t^2}{\sigma_ 1^2} \mathbf{z}_ {T,bridge} + \frac{\alpha_ t \bar{\sigma}_ t \sigma_ t}{\sigma_ 1} \\boldsymbol{\epsilon}, \boldsymbol{\epsilon} \sim \mathcal{N}(0, \mathbf{I})$ and introduces a data-informed prior, where the sampling process starts from an LR latent representation that is already informative about the HR target. This establishes a data-to-data generation trajectory.

Moreover, compared to GANs, diffusion and bridge models adopt iterative sampling, which enables the model to better capture fine-grained details, potentially leading to improved super-resolution quality.

W2: How the method might generalize to other restoration tasks or modalities

Your question is sincerely appreciated. We totally agree that more discussion of the underlying mechanisms can strengthen our contribution. Also, we provide our insights for extending this method to other restoration tasks as follows.

More discussion for generalizable training: from our perspective, bridge models are advantageous in the tasks where the condition information is instructive to the generation target. However, without a compression network, directly designing a bridge model in the waveform space or the STFT representations may increase the burden of generative models, as the redundant information in the data space has to be accurately modelled with a single generative model.

In our method, we transform the data-to-data generation process into a latent-to-latent one with a waveform compression network, which preserves the advantages of bridge models on exploiting informative prior while enabling more compact and generalizable training, allowing our AudioLBM to improve the quality across speech, audio, and music samples as shown in the subjective quality results in our Figure 1.

Extending to other restoration tasks: we think our method will be indicative to the design of bridge models on speech restoration tasks, especially the general speech restoration systems, as these tasks also require generalizable training and has indicative observation for the generation target. However, developing bridge models for these tasks should further consider their task-specific evaluation metrics, and then propose the innovative techniques suitable for these tasks.

Q1: The paper states: “We directly compress the audio waveform into a continuous latent representation, where the latent of the LR waveform provides instructive information for the HR latent and avoids the discarded regions in previous works [20, 22].” Could you supply concrete evidence for this claim? There are many ways to map a waveform into a continuous latent space, and it is not obvious that the chosen compression actually preserves the information needed to reconstruct HR audio. Any experiments comparing alternative latent encoders (e.g., raw-waveform or mel-spectrogram latents) would help substantiate the point.

Thank you for your valuable suggestion. We agree that the connection between compression strategy and the preservation of HR information should be better articulated.

However, we would like to respectfully clarify that the term "discarded regions", also referred to as "area removal", is borrowed from the recently proposed STFT-domain bridge model $A^2SB$ [1]. It describes the phenomenon in which high-frequency components are effectively discarded when using STFT or mel-spectrogram representations[2]. As the input has a lower effective frequency band, the area removal problem becomes more pronounced, making the inpainting task increasingly challenging.

We would also respectfully clarify that our discussion concerns the conceptual difference between "prior" and "condition" in the context of probabilistic generative processes, which respectively correspond to the boundary distribution of generative process (also the advantage of our bridge model compared to diffusion model) and the auxiliary indicative input of network network.

To substantiate our choice, we conduct additional experiments (see Q3) comparing waveform-based latent compression with alternatives using STFT and mel-spectrogram representations. These results confirm that our waveform latent preserves richer frequency content and leads to superior super-resolution performance.

We will make these motivations and comparisons clearer in the final version. Thank you again for helping us improve the clarity of our work, we will clarify this with more explanations in the final version.

Q2: Deeper analysis of the any-to-any process

We would like to clarify that, by defining these two conditions, our bridge models can gain a clearer understanding of the frequency boundary between the LR prior and the HR target in the bridge upsampling process. In other words, the generative process is explicitly conditioned on these two additional pieces of start and end points, enabling the model to jointly learn multiple super-resolution tasks during training. Hence, this finer-grained guidance allows the model to make more effective use of all available data (rather than relying solely on full-band inputs), and can generate desired full-band result even trained with waveforms suffered from limited effective frequency ranges, ultimately improving super-resolution performance.

Q3: Add direct comparisons with (i) latent diffusion models trained on the same latents and (ii) bridge models that operate on raw waveform or spectral representations. Such head-to-head results would clarify how much improvement truly comes from adopting a latent bridge versus alternative generative priors.

Thank you for the valuable suggestion. We agree that isolating the contribution of the latent-bridge formulation is important for a fair evaluation.

To address this, we have conducted additional experiments using the same speech datasets (OpenSLR [3], Expresso [4], EARS Dataset [5], and VCTK-Train [6]) for training all models, and evaluated them on the same VCTK-Test set.

We compare the following variants without any additional modules, each model is trained with 500K steps on the any-to-48 kHz setting and tested on 8-to-48 kHz SR setting with 50-step sampling:

• Latent Diffusion (on wav-vae latents)
• Latent Rectified Flow (on wav-vae latents)
• Bridge-STFT (Based on the Nemo[5] framework)
• Bridge-Waveform (Based on Bridge-SR[6])
• Latent Bridge (Ours)

As shown above, our latent-bridge model achieves both higher SSIM, LSD (objective quality) and SigMOS (subjective quality) score, supporting that the latent-domain bridge formulation contributes significantly to final performance, even when controlling for model architecture and training data. We also provide some corresponding visualizations in Appendix I.1 to make this clearer.

[1] A2SB: Audio-to-Audio Schrodinger Bridges. arXiv preprint arXiv:2501.11311 (2025).

[2] Time-frequency Networks for Audio Super-resolution. ICASSP, 2018

[3] Crowd-Sourced Speech Corpora for Javanese, Sundanese, Sinhala, Nepali, and Bangladeshi Bengali. SLTU, 2018.

[4] Expresso: A benchmark and analysis of discrete expressive speech resynthesis. Interspeech, 2023

[5] Speech enhancement and dereverberation with diffusion-based generative models. TASLP, 2023

[6] Expressive neural voice cloning. ACML, 2021.

[7] AudioSR: Versatile audio super-resolution at scale. ICASSP, 2024

[8] Flowhigh: Towards efficient and high-quality audio super-resolution with single-step flow matching. ICASSP, 2025

[9] ICASSP 2024 speech signal improvement challenge. IEEE Open Journal of Signal Processing, 2025

We thank the reviewer for the valuable comments. We provide a point-to-point response as follows.

Main Comments:

W1 and Q3: Motivation behind upsampling beyound 48 kHz and harmonize citation by providing all of the relevant references

We will rigorously verify and manage citations regarding the role of ultra‑high sampling rate audio. Specifically, we will address our motivation in mastering [1], post‑production [2,3], spatial audio[4], and immersive content creation[5].

As [1] shows, adopting 96 kHz permits gentler anti‑alias filters and greater headroom in the final master, albeit with higher data‑rate costs; [2] identifies near ultrasonic aliasing that intermodulates during editing and playback, advocating higher sample rates to suppress this distortion in production chains; [3] presents a meta‑analysis demonstrating a small but statistically significant perceptual advantage for high‑resolution audio under controlled listening conditions, supporting its use in critical post‑production monitoring; [4] provides psychophysical evidence that high‑frequency cues that are better preserved at ultra high sampling rates are vital for accurate spatial localization and [5] outlines coding strategies that maintain full‑bandwidth fidelity, a prerequisite for convincing, immersive playback formats.

Q1: Specify: "the prior and target frequency of sampling"

The term "frequency" here refers to the effective cut-off frequency, as defined as $\text{SR}_ {x_ {\text{HR}}}$ in Section 3.2 and explained as $f_ {\text{eff}}$ in Appendix A.1. This represents the maximum frequency containing meaningful content in the audio signal and is independent of the waveform’s sampling rate.

In our training setup, the LR signal is filtered from the HR waveform, sharing the same length. The prior and target frequencies we mention correspond to the effective cut-off frequencies of the LR and HR waveforms, respectively. These values are included as conditioning signals to enable the any-to-any super-resolution process described in Section 3.2.

We will add more explanations to clarify this in the final version.

Q2: Clarify the caption of Fig. 2

Thank you for pointing this out. To clarify:

• The top part of Figure 2 illustrates how the low-resolution waveform is simulated during training using low-pass filtering.
• The middle part corresponds to the baseline method AudioSR, which synthesizes high-resolution content from Gaussian noise.
• The bottom part presents our proposed method, AudioLBM, which defines a bridge-based trajectory between low- and high-resolution latent variables.

We will modify our caption of Figure 2 in the final version.

Q4: Specify whether the VAE is trained on LR or on HR waveform (or both)

Thank you for your valuable suggestion. Our 48 kHz VAE is trained solely on the original 48 kHz (HR) resolution waveforms,. We also experimented with supplementing the training data using low-pass-filtered (i.e., LR) versions of the same signals, but we did not observe improvements in reconstruction or super-resolution quality.

To address data scarcity at higher resolutions (96 kHz and 192 kHz), we adopt a staged training strategy, as described in Appendix B.2: we initialize the VAE with the weights from the lower sampling rate model and then fine-tune on the corresponding HR waveform data at each higher sampling rate. Please kindly visit our Appendix B for more details.

We will add more explanations on this point in the final version.

Q5: L142: "the diffusion-based audio upsampling"

The phrase "diffusion-based audio upsampling" refer specifically to the AudioSR baseline, which we use as a baseline throughout the paper illustrated in the middle part of Figure 2. We will add more explanations in the final version.

Q6: L145: Clarify "which has been aligned with"

Thank you for pointing this out. Here, "which has been aligned with" means that our boundary distributions, namely prior $z_ T^{LR}$ and target $z_ 0^{HR}$, have been aligned with the LR-to-HR task. We will make our expression more clarified in the final version.

Q7: L155: "while it has already provided", I don't understand this sentence. What does "it" refer to here?

Thank you for pointing this question out. As shown in our response to Q1, the term "it" here refers to the effective cut-off frequency, as defined in $\text{SR}_ {x_ {\text{HR}}}$ in Section 3.2 and denoted as $f_ {\text{eff}}$ with explanation in Appendix A.1. We will make our expression here clearer in the final version.

Q8: Length of HR and LR signals and potential upsampling artifacts

Thank you for your valuable suggestion. The LR signals before inference are sampled at a lower rate and therefore have shorter lengths. Figure 2 illustrates the training process of our method, in which we simulate the upsampled low-resolution waveform by directly applying a low-pass filter to the high-resolution signal. In contrast, during inference, to ensure consistency in input-output alignment and support effective inference, we first upsample the LR waveform to the target resolution by linear upsampling before feeding it into the model as outlined in line 231.

As you noted, directly performing this step may introduce artifacts, however, our method addresses this with a degradation-aware condition signal $f_ {\text{prior}}$ (see Section 3.2), which allows the model to adaptively identify the effective frequency range of the input signal and thereby mitigate the influence of such artifacts. We visualize this behavior in Appendix A.2, Figure 4, which shows how $f_ {\text{cond}}$ effectively help the model avoid artifacts during inference.

Q9: L164: Define the acronym DiT

Thank you for pointing this out. "DiT" stands for Diffusion Transformer [6] which serves as our score estimator. We will add it in the final version.

Q10: L166: why plural: "bridge models"? are several models trained?

The use of the plural form "bridge models" is intentional. In our framework, we adopt the latent scaling factor in each stage of our cascaded bridge models in Section 3.3, each responsible for performing super-resolution between three successive sampling rates. We use the plural form to indicate the cascading process.

Q11: Inference computational cost

Thank you for your valuable suggestion. Following your suggestion, we report the real-time factor (RTF) on an NVIDIA-A800 and several baselines under the 48kHz setting as follows:

It is worth noting that under the 48 kHz setting, although our method is not as fast as GAN-based approaches such as [10] and [11], because of the iterative sampling nature, it has significantly outperformed other iterative-based methods including [7], [8], and previous SoTA system AudioSR[9].

When scaling to higher sampling rates (e.g., 192 kHz), it naturally leads to slower inference speeds. Especially, we mitigate the impact by adopting a lighter network architecture, as shown in Appendix G.2, so the inference speed does not increase linearly. As shown, even upsampling to 192 kHz, it is faster than the 48 kHz waveform-domain bridge system [7].

[1] Martin Link. Digital audio at 96 khz sampling frequency-pros and cons of a new audio technique. Audio Engineering Society, 1999

[2] Richard Black. Anti-alias filters: the invisible distortion mechanism in digital audio? Audio Engineering Society, 1999.

[3] Joshua D Reiss. A meta-analysis of high resolution audio perceptual evaluation. Journal of the Audio Engineering Society, 2016

[4] Jens Blauert. Spatial hearing: the psychophysics of human sound localization. MIT press, 1997.

[5] J Robert Stuart. Coding high quality digital audio. Japan Audio Society, 1997.

[6] Scalable diffusion models with transformers. ICCV, 2023

[7] Bridge-SR: Schrödinger bridge for efficient sr. ICASSP, 2025

[8] Conditioning and sampling in variational diffusion models for speech super-resolution. ICASSP, 2023

[9] AudioSR: Versatile audio super-resolution at scale. ICASSP, 2024

[10] Audio super-resolution with robust speech representation learning of masked autoencoder. TASLP, 2024

[11] Neural vocoder is all you need for speech super-resolution. Interspeech, 2022

We thank the reviewer for the valuable comments. We provide a point-to-point response as follows.

Main Comments:

W1 and Q1: The VAE's quality

We agree that the training and performance of the VAE are central to our method. Due to the limited space of the main paper, we have provided details on its architecture and its standalone reconstruction performance in Appendix.

Specifically, we examine the reconstruction performance and its corresponding generation performance by training our model for 200K steps on each set of parameters:

• In Appendix B.1, we outline our VAE architecture and loss function, which closely follow the design and training pipeline of Stable-Audio-Open [1] and ETTA [2].
• In Appendix B.1.1, we conduct a systematic exploration of compression rates tailored to the super-resolution task, ultimately choosing a 8× compression ratio, mapping the waveform $\mathbf{x} \in \mathbb{R}^L$ to $\mathbf{z} \in \mathbb{R}^{L/512 \times 64}$.
• In Appendix B.1.2, we further investigate the influence of the KL divergence weight, providing both quantitative results and qualitative insights.
• In Appendix B.1.3, we include a detailed comparison of our VAE-based reconstructions with recent, open-sourced reconstruction baselines on 48kHz signals, as shown in our four tables in the Appendix B:

• Appendix B.2 covers the VAE training at higher resolutions (96kHz and 192kHz).

W2 and Q2: Generation process and model architecture

We would respectfully clarify that our discussion concerns the conceptual difference between "prior" and "condition" in the context of probabilistic generative processes, which respectively correspond to the boundary distribution of generative process and the auxiliary indicative input of network network.

Exploiting informative prior distribution with bridge models allows the sampling process to start from clean representations $\mathbf{z}_ {T,\text{bridge}}$ that are more instructive to the target than the noisy representations $\mathbf{z}_{T,diff} \sim \mathcal{N}(0, \mathbf{I})$ in conditional diffusion models, therefore reducing the burden of generation process and improving the generation results [7,8,9]. The condition information is provided as auxiliary model input, which can control both the noise-to-data generation direction of conditional diffusion models and the data-to-data direction of bridge models [10]. Hence, we respectfully clarify that, prior and condition are two different techniques for generative models, and improve the generation results from different perspectives. More details can be visited in following references: bridge models [7,8,9], and conditional diffusion models [10].

In audio super-resolution (i.e., LR-to-HR) task, as the LR observation has already provided instructive information for the HR target, we naturally improve previous noise-to-data generation process with the data-to-data one in bridge models, aligning our boundary distributions with the LR-to-HR task. Namely, both AudioSR and our AudioLBM contain condition information ,i.e., the LR obversation. Hence, the advantages of our method lie in the constructed transition trajectory between LR and HR pairs, which fully exploits the informative LR prior, rather than the external condition that encoded by specific model architecture.

Previously, in AudioSR, the prior $\mathbf{z}_ {T,diff}$ is drawn from a standard Gaussian distribution $\mathcal{N}(0, I)$ which is not informative to the HR target. The diffusion trajectory is defined as: $\mathbf{z}_ {t,diff} = \alpha(t) \cdot \mathbf{z}_ 0 + \beta(t) \cdot \boldsymbol{\epsilon}, \boldsymbol{\epsilon} \sim \mathcal{N}(0, \mathbf{I}),$ where the sampling process starts from $\mathbf{z}_ {T,diff} \approx \boldsymbol{\epsilon}$ and can not exploit instructive LR as prior for generative process, forcing the model to reconstruct the full HR target purely via sampling from noise.

In contrast, our AudioLBM uses a bridge process, where the trajectory is explicitly defined between informative latent variables. Specifically, our formulation is: $\mathbf{z}_ {t,bridge} = \frac{\alpha_ t \bar{\sigma}_ t^2}{\sigma_ 1^2} \mathbf{z}_ 0+ \frac{\bar{\alpha}_ t \sigma_ t^2}{\sigma_ 1^2} \mathbf{z}_ {T,bridge} + \frac{\alpha_ t \bar{\sigma}_ t \sigma_ t}{\sigma_ 1} \boldsymbol{\epsilon}, \boldsymbol{\epsilon} \sim \mathcal{N}(0, \mathbf{I})$. Here, the intermediate latent representations $\mathbf{z}_ {t,bridge}$ has been a stochatisc interpolation between the HR latent $\mathbf{z}_ 0$ and the LR latent $\mathbf{z}_ {T,bridge}$, which allows the generative process to exploit the informative LR latent.

Therefore, despite the ability of architectures like Transformer or U-Net to extract and utilize low-frequency condition, their generative process uses uninformative Gaussian prior, which may lead to sub-optimal performance on audio super-resolution task. Namely, their sampling initiates denoising from Gaussian noise, resulting in a noise-to-data generation process whose boundary distributions are misaligned with the LR-to-HR up-sampling task.

We will clarify this with more explanations in the final version.

W3 and Q3: Explanation of "area removal"

Thank you for point that out. We would respectfully clarify that the term "area removal" is leveraged from recently proposed STFT-domain bridge model $A^2SB$ [11], refering to the phenomenon where high-frequency components are effectively filtered when using STFT or mel-spectrogram representations.

To elaborate, audio super-resolution aims to recover high-frequency components that are missing from low-resolution waveforms. In the frequency domain (e.g., STFT or mel-spectrogram), this typically manifests as blank or attenuated regions in the upper part of the spectrum, as illustrated in Line 51 of our submission and reference [12].

We will add more explanations to make this clearer in the final version.

W4 and Q4: Explanation of Figure 2, $z^{HR}$ and $z^{LR}$

Figure 2 illustrates the training pipeline, in which the HR waveform is passed through a low-pass filter to simulate the LR signal. This filtering process preserves the temporal duration of the waveform, meaning that both HR and LR waveforms have the same length during training. To clarify:

• The top part of Figure 2 illustrates how the low-resolution waveform is simulated during training using low-pass filtering.
• The middle part corresponds to the baseline method AudioSR, which synthesizes high-resolution target from uninformative Gaussian noise.
• The bottom part presents our proposed method, AudioLBM, which defines a bridge-based trajectories between informative LR and HR Wav-VAE latents.

Before inference, observed LR representation are typically shorter than the target HR represenatation in length due to lower sampling rate. To bridge this gap between inference and training, we linearly upsample observed signal to the LR prior in the waveform space, matching the target HR waveform length before compressing them into the latent space. This ensures temporal alignment and avoids train-test mismatch. This strategy is briefly mentioned in Section 4.1 ("Training Setup"), and we will add more explanations to clarify this in the final version and make it more explicit in the experiment section to aid understanding of both the training and inference procedures.

[1] Stable Audio Open. ICASSP, 2025.

[2] ETTA: Elucidating the Design Space of Text-to-Audio Models. ICML, 2025

[3] AudiogenAI. AGC: Audio Generative Compression. Github Repo, 2024

[4] High Fidelity Neural Audio Compression. TMLR, 2023.

[5] Audiodec: An Open-source Streaming High-fidelity Neural Audio Codec. ICASSP, 2023

[6] FlowDec: A Flow-based Full-band General Audio Codec with High Perceptual Quality. ICLR, 2025

[7] Denoising Diffusion Bridge Models. ICLR, 2024

[8] I2SB: image-to-image Schrödinger bridge. ICML, 2023

[9] Schrödinger bridges beat diffusion models on text-to-speech synthesis. arXiv:2312.03491 (2023)

[10] Why are conditional generative models better than unconditional ones?. NeurIPSW, 2022

[11] A2SB: Audio-to-Audio Schrodinger Bridges. arXiv:2501.11311 (2025)

[12] Time-frequency Networks for Audio Super-resolution. ICASSP, 2018

I would like to thank the authors for the responses, I have adjusted my score.

We sincerely thank the reviewer for the thoughtful follow-up and for acknowledging our clarifications regarding the VAE details (W1/Q1), as well as the willingness to raise the score. We greatly appreciate the opportunity to further clarify the remaining points.

W2 and Q2: Motivation of bridge process

We appreciate your thoughtful feedback and agree that the original wording may have overstated the issue. Our intention was not to imply that prior work entirely ignores information from the LR representation, but rather to highlight a distinction in how this information is utilize for generative trajectory. Specifically, existing approaches often leverage the LR signal for conditioning, but do not explicitly incorporate it into the latent prior distribution itself. Our proposed bridge framework aims to better utilize this information by aligning the LR-informed latent prior with the HR target distribution, thereby enabling more effective learning and sampling trajectories. To clarify our point, we will revise the statement in the final version to: “While prior methods condition on the LR signal or learn priors independently, they often overlook that the LR waveform carries informative cues that can be integrated into the latent prior. This may lead to sub-optimal probability trajectories during generation.”

W3 and Q3: Explanation of "area removal

Thank you for the question. You are right that the STFT is a nearly lossless transform for discrete-time signals. However, our use of the term "area removal" was not meant to suggest information loss caused by the representation (like STFT or Mel) itself, but rather to describe the representational consequence of low-pass filtering in spectral domains, which serves the input signal in our SR task. Specifically, in A2SB[1] (Section 3.2, line 5), "area removal" refers to the phenomenon where high-frequency filtering of the waveform manifests as an energy void in the upper region of its spectrogram—visually resembling a blanked-out area. Crucially, this effect stems from the filtering operation, not the spectral transform. The same logic applies to mel-spectrograms: the "removed area" reflects the filtering-induced absence of high-frequency energy, not compression from mel-filterbanks. We will clarify this distinction in the final version.

[1] A2SB: Audio-to-Audio Schrodinger Bridges. arXiv:2501.11311 (2025)