# Bridging the Discrete-Continuous Gap: Unified Multimodal Generation via Coupled Manifold Discrete Absorbing Diffusion

arXiv: https://arxiv.org/abs/2601.04056 · HTML: https://mlsanity.com/paper/2601.04056/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Image generation, text-to-image and editing, one of 14 directions in Diffusion models.
- Builds on 23 of its 31 references that are in the map.
- First posted on arXiv 7 Jan 2026.

## Placed in

- Diffusion models / [Image generation, text-to-image and editing](https://mlsanity.com/diffusion/image-generation-text-to-image-and-editing/)

## Builds on (most cited first, 23 of 23)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [An Empirical Study of Training Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.02057/) (2021)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Chameleon: Mixed-Modal Early-Fusion Foundation Models](https://mlsanity.com/paper/2405.09818/) (2024)
- [Vector-quantized Image Modeling with Improved VQGAN](https://mlsanity.com/paper/2110.04627/) (2021)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [Texygen: A Benchmarking Platform for Text Generation Models](https://mlsanity.com/paper/1802.01886/) (2018)
- [Fast-dLLM: Training-free Acceleration of Diffusion LLM by Enabling KV Cache and Parallel Decoding](https://mlsanity.com/paper/2505.22618/) (2025)
- [PaLI-X: On Scaling up a Multilingual Vision and Language Model](https://mlsanity.com/paper/2305.18565/) (2023)
- [MAGE: MAsked Generative Encoder to Unify Representation Learning and Image Synthesis](https://mlsanity.com/paper/2211.09117/) (2022)
- [DiffusionBERT: Improving Generative Masked Language Models with Diffusion Models](https://mlsanity.com/paper/2211.15029/) (2022)
- [BERT has a Mouth, and It Must Speak: BERT as a Markov Random Field Language Model](https://mlsanity.com/paper/1902.04094/) (2019)
- [Instance-Conditioned GAN](https://mlsanity.com/paper/2109.05070/) (2021)
- [Should You Mask 15% in Masked Language Modeling?](https://mlsanity.com/paper/2202.08005/) (2022)
- [Return of Unconditional Generation: A Self-supervised Representation Generation Method](https://mlsanity.com/paper/2312.03701/) (2023)
- [ADDP: Learning General Representations for Image Recognition and Generation with Alternating Denoising Diffusion Process](https://mlsanity.com/paper/2306.05423/) (2023)
- [Traditional Classification Neural Networks are Good Generators: They are Competitive with DDPMs and GANs](https://mlsanity.com/paper/2211.14794/) (2022)
- [In-Situ Tweedie Discrete Diffusion Models](https://mlsanity.com/paper/2510.01047/) (2025)

## Built on by (most cited first, 1 of 1)

- [OOWM: Structuring Embodied Reasoning and Planning via Object-Oriented Programmatic World Modeling](https://mlsanity.com/paper/2604.09580/) (2026)

## Abstract (arXiv)

The bifurcation of generative modeling into autoregressive approaches for discrete data (text) and diffusion approaches for continuous data (images) hinders the development of truly unified multimodal systems. While Masked Language Models (MLMs) offer efficient bidirectional context, they traditionally lack the generative fidelity of autoregressive models and the semantic continuity of diffusion models. Furthermore, extending masked generation to multimodal settings introduces severe alignment challenges and training instability. In this work, we propose CoM-DAD (Coupled Manifold Discrete Absorbing Diffusion), a novel probabilistic framework that reformulates multimodal generation as a hierarchical dual-process. CoM-DAD decouples high-level semantic planning from low-level token synthesis. First, we model the semantic manifold via a continuous latent diffusion process; second, we treat token generation as a discrete absorbing diffusion process, regulated by a Variable-Rate Noise Schedule, conditioned on these evolving semantic priors. Crucially, we introduce a Stochastic Mixed-Modal Transport strategy that aligns disparate modalities without requiring heavy contrastive dual-encoders. Our method demonstrates superior stability over standard masked modeling, establishing a new paradigm for scalable, unified text-image generation.