# InferGrad: Improving Diffusion Models for Vocoder by Considering Inference in Training

arXiv: https://arxiv.org/abs/2202.03751 · HTML: https://mlsanity.com/paper/2202.03751/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 25 of its 31 references that are in the map.
- First posted on arXiv 8 Feb 2022.

## Placed in

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

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [HiFi-GAN: Generative Adversarial Networks for Efficient and High Fidelity Speech Synthesis](https://mlsanity.com/paper/2010.05646/) (2020)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speech](https://mlsanity.com/paper/2105.06337/) (2021)
- [MelGAN: Generative Adversarial Networks for Conditional Waveform Synthesis](https://mlsanity.com/paper/1910.06711/) (2019)
- [Parallel WaveGAN: A fast waveform generation model based on generative adversarial networks with multi-resolution spectrogram](https://mlsanity.com/paper/1910.11480/) (2019)
- [Efficient Neural Audio Synthesis](https://mlsanity.com/paper/1802.08435/) (2018)
- [Parallel WaveNet: Fast High-Fidelity Speech Synthesis](https://mlsanity.com/paper/1711.10433/) (2017)
- [A Survey on Neural Speech Synthesis](https://mlsanity.com/paper/2106.15561/) (2021)
- [SampleRNN: An Unconditional End-to-End Neural Audio Generation Model](https://mlsanity.com/paper/1612.07837/) (2016)
- [Noise Estimation for Generative Diffusion Models](https://mlsanity.com/paper/2104.02600/) (2021)
- [High Fidelity Speech Synthesis with Adversarial Networks](https://mlsanity.com/paper/1909.11646/) (2019)
- [Bilateral Denoising Diffusion Models](https://mlsanity.com/paper/2108.11514/) (2021)

## Built on by (most cited first, 28 of 28)

- [AudioLDM: Text-to-Audio Generation with Latent Diffusion Models](https://mlsanity.com/paper/2301.12503/) (2023)
- [AudioLDM 2: Learning Holistic Audio Generation with Self-supervised Pretraining](https://mlsanity.com/paper/2308.05734/) (2023)
- [A Survey on Generative Diffusion Model](https://mlsanity.com/paper/2209.02646/) (2022)
- [Noise2Music: Text-conditioned Music Generation with Diffusion Models](https://mlsanity.com/paper/2302.03917/) (2023)
- [StyleTTS 2: Towards Human-Level Text-to-Speech through Style Diffusion and Adversarial Training with Large Speech Language Models](https://mlsanity.com/paper/2306.07691/) (2023)
- [A Complete Survey on Generative AI (AIGC): Is ChatGPT from GPT-4 to GPT-5 All You Need?](https://mlsanity.com/paper/2303.11717/) (2023)
- [A Survey on Audio Diffusion Models: Text To Speech Synthesis and Enhancement in Generative AI](https://mlsanity.com/paper/2303.13336/) (2023)
- [RenAIssance: A Survey into AI Text-to-Image Generation in the Era of Large Model](https://mlsanity.com/paper/2309.00810/) (2023)
- [BinauralGrad: A Two-Stage Conditional Diffusion Probabilistic Model for Binaural Audio Synthesis](https://mlsanity.com/paper/2205.14807/) (2022)
- [SpecGrad: Diffusion Probabilistic Model based Neural Vocoder with Adaptive Noise Spectral Shaping](https://mlsanity.com/paper/2203.16749/) (2022)
- [Enhancing Diffusion-Based Image Synthesis with Robust Classifier Guidance](https://mlsanity.com/paper/2208.08664/) (2022)
- [Schrodinger Bridges Beat Diffusion Models on Text-to-Speech Synthesis](https://mlsanity.com/paper/2312.03491/) (2023)
- [Generating Visual Scenes from Touch](https://mlsanity.com/paper/2309.15117/) (2023)
- [ResGrad: Residual Denoising Diffusion Probabilistic Models for Text to Speech](https://mlsanity.com/paper/2212.14518/) (2022)
- [WaveFit: An Iterative and Non-autoregressive Neural Vocoder based on Fixed-Point Iteration](https://mlsanity.com/paper/2210.01029/) (2022)
- [FreGrad: Lightweight and Fast Frequency-aware Diffusion Vocoder](https://mlsanity.com/paper/2401.10032/) (2024)
- [Reconstruction of Sound Field through Diffusion Models](https://mlsanity.com/paper/2312.08821/) (2023)
- [Two-Steps Diffusion Policy for Robotic Manipulation via Genetic Denoising](https://mlsanity.com/paper/2510.21991/) (2025)
- [Improving Diffusion Models for ECG Imputation with an Augmented Template Prior](https://mlsanity.com/paper/2310.15742/) (2023)
- [Versatile Cardiovascular Signal Generation with a Unified Diffusion Transformer](https://mlsanity.com/paper/2505.22306/) (2025)
- [SonicVisionLM: Playing Sound with Vision Language Models](https://mlsanity.com/paper/2401.04394/) (2024)
- [PeriodGrad: Towards Pitch-Controllable Neural Vocoder Based on a Diffusion Probabilistic Model](https://mlsanity.com/paper/2402.14692/) (2024)
- [LiteFocus: Accelerated Diffusion Inference for Long Audio Synthesis](https://mlsanity.com/paper/2407.10468/) (2024)
- [DreamAudio: Customized Text-to-Audio Generation with Diffusion Models](https://mlsanity.com/paper/2509.06027/) (2025)
- [GuidedBridge: Training-freely Improving Bridge Models with Prior Guidance](https://mlsanity.com/paper/2606.03119/) (2026)
- [FastFit: Towards Real-Time Iterative Neural Vocoder by Replacing U-Net Encoder With Multiple STFTs](https://mlsanity.com/paper/2305.10823/) (2023)
- [DPI-TTS: Directional Patch Interaction for Fast-Converging and Style Temporal Modeling in Text-to-Speech](https://mlsanity.com/paper/2409.11835/) (2024)
- [SR-Edit: Region-Aware Image Editing via Self-Refinement](https://mlsanity.com/paper/2609.02504/) (2026)

## Abstract (arXiv)

Denoising diffusion probabilistic models (diffusion models for short) require a large number of iterations in inference to achieve the generation quality that matches or surpasses the state-of-the-art generative models, which invariably results in slow inference speed. Previous approaches aim to optimize the choice of inference schedule over a few iterations to speed up inference. However, this results in reduced generation quality, mainly because the inference process is optimized separately, without jointly optimizing with the training process. In this paper, we propose InferGrad, a diffusion model for vocoder that incorporates inference process into training, to reduce the inference iterations while maintaining high generation quality. More specifically, during training, we generate data from random noise through a reverse process under inference schedules with a few iterations, and impose a loss to minimize the gap between the generated and ground-truth data samples. Then, unlike existing approaches, the training of InferGrad considers the inference process. The advantages of InferGrad are demonstrated through experiments on the LJSpeech dataset showing that InferGrad achieves better voice quality than the baseline WaveGrad under same conditions while maintaining the same voice quality as the baseline but with 3x speedup (2 iterations for InferGrad vs 6 iterations for WaveGrad).