# Improving Vector-Quantized Image Modeling with Latent Consistency-Matching Diffusion

arXiv: https://arxiv.org/abs/2410.14758 · HTML: https://mlsanity.com/paper/2410.14758/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 49 of its 56 references that are in the map.
- First posted on arXiv 18 Oct 2024.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 49)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (2021)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Muse: Text-To-Image Generation via Masked Generative Transformers](https://mlsanity.com/paper/2301.00704/) (2023)

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

- [CANDI: Hybrid Discrete-Continuous Diffusion Models](https://mlsanity.com/paper/2510.22510/) (2025)
- [Stochastic and Non-local Closure Modeling for Nonlinear Dynamical Systems via Latent Score-based Generative Models](https://mlsanity.com/paper/2506.20771/) (2025)
- [Optimality of FSQ Tokens for Continuous Diffusion for Categorical Data with Application to Text-to-Speech](https://mlsanity.com/paper/2606.09962/) (2026)
- [Conservation Laws for Diffusion Models](https://mlsanity.com/paper/2607.10067/) (2026)
- [Bernoulli Flow Models: Self-Consistent Generative Modeling for Binary Data](https://mlsanity.com/paper/2610.11362/) (2026)

## Abstract (arXiv)

By embedding discrete representations into a continuous latent space, we can leverage continuous-space latent diffusion models to handle generative modeling of discrete data. However, despite their initial success, most latent diffusion methods rely on fixed pretrained embeddings, limiting the benefits of joint training with the diffusion model. While jointly learning the embedding (via reconstruction loss) and the latent diffusion model (via score matching loss) could enhance performance, end-to-end training risks embedding collapse, degrading generation quality. To mitigate this issue, we introduce VQ-LCMD, a continuous-space latent diffusion framework within the embedding space that stabilizes training. VQ-LCMD uses a novel training objective combining the joint embedding-diffusion variational lower bound with a consistency-matching (CM) loss, alongside a shifted cosine noise schedule and random dropping strategy. Experiments on several benchmarks show that the proposed VQ-LCMD yields superior results on FFHQ, LSUN Churches, and LSUN Bedrooms compared to discrete-state latent diffusion models. In particular, VQ-LCMD achieves an FID of 6.81 for class-conditional image generation on ImageNet with 50 steps.