Recursive Scaling in Masked Diffusion Models
cs.LG
Submitted: 2026-06-16
Updated: 2026-09-28
License: http://creativecommons.org/licenses/by/4.0/
The gist: Masked diffusion models (MDMs) generate sequences by iteratively refining a partially masked state and committing tokens in parallel.
Terminology
Abstract
Masked diffusion models (MDMs) generate sequences by iteratively refining a partially masked state and committing tokens in parallel. We introduce recursion in MDMs and propose new Recursive Masked Diffusion Models (R-MDMs), which apply a shared denoising transformer L times within each denoising step, adding recursive depth as an additional compute axis without increasing parameter count. Across structured generation tasks, recursive depth improves quality at fixed parameter budget, matches substantially larger non-recursive models at matched FLOPs, and can reduce the number of denoising steps needed to reach a target quality. We interpret these gains with a dependence--fidelity decomposition of parallel decoding error: recursion refines model marginals at a fixed masked state, whereas denoising steps change that state by committing tokens. Building on this analysis, we propose to treat decoding as a two-axis decision (how many loops to run and which tokens to commit) and show that entropy-guided adaptive rules improve the quality--compute frontier over fixed schedules, transferring across various tasks on Sudoku, Countdown, RNA, and executable math generation. Together, these results establish recursive depth as a practical, complementary test-time scaling mechanism for MDMs.
Sources
- Structured Denoising Diffusion Models in Discrete State-Spaces
- Accelerated Sampling from Masked Diffusion Models via Entropy Bounded Unmasking
- A Mechanistic Analysis of Looped Reasoning Language Models
- Confidence-Based Decoding is Provably Efficient for Diffusion Language Models
- MaskGIT: Masked Generative Image Transformer
- Training Verifiers to Solve Math Word Problems
- Universal Transformers
- LT2: Linear-Time Looped Transformers
- DiffusionGemma Technical Report
- Looped Transformers for Length Generalization
- Learning Generation Orders for Masked Discrete Diffusion Models via Variational Inference
- Stream of Search (SoS): Learning to Search in Language
- Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach
- Looped Transformers as Programmable Computers
- Reasoning with Latent Tokens in Diffusion Language Models
- Denoising Diffusion Probabilistic Models
- Learning Anytime Predictions in Neural Networks via Adaptive Loss Balancing
- Recursive Flow Matching
- Scaling Laws for Neural Language Models
- Flow Map Language Models: One-step Language Modeling via Continuous Denoising
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