# DiVeQ: Differentiable Vector Quantization Using the Reparameterization Trick

arXiv: https://arxiv.org/abs/2509.26469 · HTML: https://mlsanity.com/paper/2509.26469/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 57 references that are in the map.
- First posted on arXiv 30 Sep 2025.

## Builds on (most cited first, 30 of 42)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [SoundStream: An End-to-End Neural Audio Codec](https://mlsanity.com/paper/2107.03312/) (2021)
- [Autoregressive Image Generation using Residual Quantization](https://mlsanity.com/paper/2203.01941/) (2022)
- [VideoGPT: Video Generation using VQ-VAE and Transformers](https://mlsanity.com/paper/2104.10157/) (2021)
- [Vector-quantized Image Modeling with Improved VQGAN](https://mlsanity.com/paper/2110.04627/) (2021)
- [Language Model Beats Diffusion -- Tokenizer is Key to Visual Generation](https://mlsanity.com/paper/2310.05737/) (2023)
- [Jukebox: A Generative Model for Music](https://mlsanity.com/paper/2005.00341/) (2020)
- [Finite Scalar Quantization: VQ-VAE Made Simple](https://mlsanity.com/paper/2309.15505/) (2023)
- [High-Fidelity Audio Compression with Improved RVQGAN](https://mlsanity.com/paper/2306.06546/) (2023)
- [Latent Action Pretraining from Videos](https://mlsanity.com/paper/2410.11758/) (2024)
- [PeCo: Perceptual Codebook for BERT Pre-training of Vision Transformers](https://mlsanity.com/paper/2111.12710/) (2021)
- [Self-supervised Learning with Random-projection Quantizer for Speech Recognition](https://mlsanity.com/paper/2202.01855/) (2022)
- [Soft-to-Hard Vector Quantization for End-to-End Learning Compressible Representations](https://mlsanity.com/paper/1704.00648/) (2017)
- [Image and Video Tokenization with Binary Spherical Quantization](https://mlsanity.com/paper/2406.07548/) (2024)
- [Straightening Out the Straight-Through Estimator: Overcoming Optimization Challenges in Vector Quantized Networks](https://mlsanity.com/paper/2305.08842/) (2023)
- [UViM: A Unified Modeling Approach for Vision with Learned Guiding Codes](https://mlsanity.com/paper/2205.10337/) (2022)
- [SQ-VAE: Variational Bayes on Discrete Representation with Self-annealed Stochastic Quantization](https://mlsanity.com/paper/2205.07547/) (2022)
- [Towards Accurate Image Coding: Improved Autoregressive Image Generation with Dynamic Vector Quantization](https://mlsanity.com/paper/2305.11718/) (2023)
- [Online Clustered Codebook](https://mlsanity.com/paper/2307.15139/) (2023)

## Built on by (most cited first, 5 of 5)

- [Online Vector Quantized Attention](https://mlsanity.com/paper/2602.03922/) (2026)
- [Divide et Calibra: Multiclass Local Calibration via Vector Quantization](https://mlsanity.com/paper/2605.21060/) (2026)
- [AVQ-Attention: Adaptive Vector-Quantized Attention](https://mlsanity.com/paper/2607.12789/) (2026)
- [Generalized Radius and Integrated Codebook Transforms for Differentiable Vector Quantization](https://mlsanity.com/paper/2602.01140/) (2026)
- [What Makes a Good Medical Image Tokenizer? Rethinking Reconstruction and Generation in Medical Image Tokenization](https://mlsanity.com/paper/2609.24691/) (2026)

## Abstract (arXiv)

Vector quantization is common in deep models, yet its hard assignments block gradients and hinder end-to-end training. We propose DiVeQ, which treats quantization as adding an error vector that mimics the quantization distortion, keeping the forward pass hard while letting gradients flow. We also present a space-filling variant (SF-DiVeQ) that assigns input to a curve constructed by the lines connecting codewords, resulting in less quantization error and full codebook usage. Both methods train end-to-end without requiring auxiliary losses or temperature schedules. In VQ-VAE image compression, VQGAN image generation, and DAC speech coding tasks across various data sets, our proposed methods improve reconstruction and sample quality over alternative quantization approaches.