# Conditioning and Sampling in Variational Diffusion Models for Speech Super-Resolution

arXiv: https://arxiv.org/abs/2210.15793 · HTML: https://mlsanity.com/paper/2210.15793/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 18 of its 23 references that are in the map.
- First posted on arXiv 27 Oct 2022.

## Placed in

- Diffusion models / [Audio, speech and music](https://mlsanity.com/diffusion/audio-speech-and-music/)

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [WaveGlow: A Flow-based Generative Network for Speech Synthesis](https://mlsanity.com/paper/1811.00002/) (2018)
- [Speech Enhancement with Score-Based Generative Models in the Complex STFT Domain](https://mlsanity.com/paper/2203.17004/) (2022)
- [A Study on Speech Enhancement Based on Diffusion Probabilistic Model](https://mlsanity.com/paper/2107.11876/) (2021)
- [NU-Wave: A Diffusion Probabilistic Model for Neural Audio Upsampling](https://mlsanity.com/paper/2104.02321/) (2021)
- [Neural Vocoder is All You Need for Speech Super-resolution](https://mlsanity.com/paper/2203.14941/) (2022)
- [NU-Wave 2: A General Neural Audio Upsampling Model for Various Sampling Rates](https://mlsanity.com/paper/2206.08545/) (2022)
- [WSRGlow: A Glow-based Waveform Generative Model for Audio Super-Resolution](https://mlsanity.com/paper/2106.08507/) (2021)

## Built on by (most cited first, 20 of 20)

- [An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization](https://mlsanity.com/paper/2404.07771/) (2024)
- [A Survey on Audio Diffusion Models: Text To Speech Synthesis and Enhancement in Generative AI](https://mlsanity.com/paper/2303.13336/) (2023)
- [Multi-Source Diffusion Models for Simultaneous Music Generation and Separation](https://mlsanity.com/paper/2302.02257/) (2023)
- [HierSpeech++: Bridging the Gap between Semantic and Acoustic Representation of Speech by Hierarchical Variational Inference for Zero-shot Speech Synthesis](https://mlsanity.com/paper/2311.12454/) (2023)
- [Blind Audio Bandwidth Extension: A Diffusion-Based Zero-Shot Approach](https://mlsanity.com/paper/2306.01433/) (2023)
- [FLowHigh: Towards Efficient and High-Quality Audio Super-Resolution with Single-Step Flow Matching](https://mlsanity.com/paper/2501.04926/) (2025)
- [Audio Super-Resolution with Latent Bridge Models](https://mlsanity.com/paper/2509.17609/) (2025)
- [A2SB: Audio-to-Audio Schrodinger Bridges](https://mlsanity.com/paper/2501.11311/) (2025)
- [Reconstruction of Sound Field through Diffusion Models](https://mlsanity.com/paper/2312.08821/) (2023)
- [Naturalistic Music Decoding from EEG Data via Latent Diffusion Models](https://mlsanity.com/paper/2405.09062/) (2024)
- [Thompson Sampling with Diffusion Generative Prior](https://mlsanity.com/paper/2301.05182/) (2023)
- [mdctGAN: Taming transformer-based GAN for speech super-resolution with Modified DCT spectra](https://mlsanity.com/paper/2305.11104/) (2023)
- [Zero-Shot Duet Singing Voices Separation with Diffusion Models](https://mlsanity.com/paper/2311.07345/) (2023)
- [Inference-time Scaling for Diffusion-based Audio Super-resolution](https://mlsanity.com/paper/2508.02391/) (2025)
- [UniverSR: Unified and Versatile Audio Super-Resolution via Vocoder-Free Flow Matching](https://mlsanity.com/paper/2510.00771/) (2025)
- [MSECG: Incorporating Mamba for Robust and Efficient ECG Super-Resolution](https://mlsanity.com/paper/2412.04861/) (2024)
- [LatentFlowSR: High-Fidelity Audio Super-Resolution via Noise-Robust Latent Flow Matching](https://mlsanity.com/paper/2604.09188/) (2026)
- [Improving Inference-Time Optimisation for Vocal Effects Style Transfer with a Gaussian Prior](https://mlsanity.com/paper/2505.11315/) (2025)
- [FastWave: Optimized Diffusion Model for Audio Super-Resolution](https://mlsanity.com/paper/2603.04122/) (2026)
- [P2Flow: Phoneme-aware Progressive Flow Matching for Extreme Speech Super-Resolution](https://mlsanity.com/paper/2609.24138/) (2026)

## Abstract (arXiv)

Recently, diffusion models (DMs) have been increasingly used in audio processing tasks, including speech super-resolution (SR), which aims to restore high-frequency content given low-resolution speech utterances. This is commonly achieved by conditioning the network of noise predictor with low-resolution audio. In this paper, we propose a novel sampling algorithm that communicates the information of the low-resolution audio via the reverse sampling process of DMs. The proposed method can be a drop-in replacement for the vanilla sampling process and can significantly improve the performance of the existing works. Moreover, by coupling the proposed sampling method with an unconditional DM, i.e., a DM with no auxiliary inputs to its noise predictor, we can generalize it to a wide range of SR setups. We also attain state-of-the-art results on the VCTK Multi-Speaker benchmark with this novel formulation.