Group 2: the diffusion-LLM line

Read these five in this order — each solves a problem the previous one exposes.

1. Masked Diffusion — MDLM (Sahoo et al., 2024)

Simple and Effective Masked Diffusion Language Models is the workhorse recipe — the entire Maths II section up to the extensions. Its contributions: the SUBS parameterization that Rao-Blackwellizes the bound, the clean weighted-MLM continuous-time objective, and the schedule-invariance theorem. With them, masked diffusion went from mathematically intricate and badly lagging to simple and nearly perplexity-competitive with AR training — the proof that the approach deserved scaling.

2. Block Diffusion — BD3-LM (Arriola et al., 2025)

Vanilla masked diffusion paints on a fixed-size canvas and re-reads the whole canvas every pass, forfeiting KV caching. Block Diffusion puts the AR chain rule at block granularity — ∑_b L_MDLM(x^(b) | x^(<b)) — so each block diffuses in parallel while conditioning on cached previous blocks.

Block 1done · cached

→

Block 2diffusing in parallel now

→

Block 3not started

Autoregressive across blocks (variable length, KV caching), diffusion within blocks (parallel speed). Block size 1 is pure AR; block size = sequence length is vanilla diffusion; production lives in between.

3. Remasking Diffusion — ReMDM (Wang et al., 2025)

Remasking Discrete Diffusion Models fixes the frozen-token theorem: a modified sampler kernel that returns committed tokens to [MASK] with probability σ_t, constructed to preserve the forward marginals — which is precisely why it needs no retraining. This is what makes a dLLM a true editor, and it gives dLLMs an inference-time scaling law: more sampling steps → more self-correction → measurably better text.

4. Discrete Diffusion Guidance (Schiff et al., 2024)

Simple Guidance Mechanisms for Discrete Diffusion Models ports image diffusion’s best control trick to discrete data: the γ-exponentiated conditional/unconditional ratio derived in Maths III, applied per position per step, plus a classifier-based variant for when no conditional model exists. Turn γ and you push generation toward a sentiment, a style, or drug-likeness when the “tokens” are molecule fragments — at sampling time, no retraining.

5. d1 Reasoning (Zhao et al., 2025)

d1 (from Grover’s lab) answers the frontier-relevance question: can dLLMs do the long chain-of-thought reasoning that made o1-style models famous? The recipe: supervised fine-tuning on worked reasoning traces, then diffu-GRPO — the one-step log-prob estimator and group-relative advantages derived in Maths III. It works: reasoning improves substantially, showing the modern capability playbook transfers to diffusion. Note the pleasing symmetry with the foundations group: RL-as-sequence-modeling (Decision Transformer) and preference training (DPO) were both founder groundwork for this step.

← Group 1: the foundations How it adds up →