CASCADE descends from a specific set of 13 papers. Each note follows a uniform five-section template: corruption process, loss, inference structure, KV-cache use, throughput vs AR comparison. The two anchors (LLaDA and BD3-LM) are fully drafted; the other 11 are structured stubs flagged for verification against the actual papers.
A note on verification status
The stub notes draw from training-data memory of the cited papers. Every numeric claim is marked [verify] or TBD. Before any claim in a stub note enters a downstream document (a decision log, the eventual paper, or external talks), the note should be promoted to verified by reading the actual paper.
First masked-diffusion LM trained from scratch at 8B parameters, matching LLaMA-3 8B on standard benchmarks. The strongest single piece of evidence that the whole CASCADE thesis is sound. Loss recipe (per-sequence m ∈ U[0, 1], 1/m-weighted CE on masked positions) is inherited directly. Critically, LLaDA's throughput does not grow with sequence length — the structural block-diffusion fix is what CASCADE bets on.
The architectural ancestor CASCADE descends from most directly. Interpolates AR and full masked diffusion via a single knob — the block size B. At B = 1 it is exactly AR; at B = L it is exactly LLaDA-style full masked diffusion; intermediate B (~32) Pareto-dominates both endpoints. CASCADE adds two deltas: adaptive per-block step count (BD3-LM uses fixed K) and AR-to-CASCADE distillation (BD3-LM trains from scratch).
The foundational paper for discrete-state diffusion. The absorbing-state variant — gradually replacing tokens with [MASK] — is the direct ancestor of LLaDA, BD3-LM, and CASCADE. The ELBO derivation here is the principled justification for the 1/m reweighting.
Alternative loss formulation via score matching for discrete state spaces. Important as a competing theoretical framing; ablation possibility for CASCADE if the LLaDA-style CE loss underperforms.
The cleanest re-derivation: linear absorbing schedule m(t) = t gives the 1/m-weighted CE loss as the negative ELBO. CASCADE's training loss is literally MD4's loss applied per-block.
Family of LLaDA follow-ups: multimodal (V), MoE, dense scaling. Robustness evidence — masked diffusion works across scales and architecture additions.
The blueprint for CASCADE Phase 4. Starts from Qwen-2.5-7B and continues pretraining on the masked-diffusion objective for ~150B tokens, recovering most of the AR teacher's quality at a fraction of the from-scratch cost.
Training-free accelerator for masked-diffusion LMs: caches K/V at committed positions across denoising steps. The within-block analog of CASCADE's across-block cache. The structural threat: if Fast-dLLM v2 alone is fast enough, CASCADE's pitch must lean on streaming preservation.
The 2022 antecedent to BD3-LM, in continuous (simplex) state space. Historical interest: BD3-LM cites it as the precedent for block diffusion. Mostly relevant as a “why discrete-state won” data point.
The closest analog to CASCADE's thesis in the video domain — convert bidirectional diffusion to AR-along-one-axis. Cross-modal validation of the “block-causal + diffusion-within-block” pattern.
2025 field survey. Useful for coverage check (anything cited but missing from CASCADE's lit set is a gap) and for the related-work matrix in Phase 6's paper.
The first production-deployed diffusion language model, with advertised very-large throughput multiples. The visible competitive benchmark for CASCADE. Open question: is Mercury block-diffusion (in which case CASCADE's adaptive-K is the only delta) or full diffusion + Fast-dLLM-style cache (in which case streaming is the differentiator)?
The empirical evidence for the block-size knob. Sweeps B from 1 (= AR) to L (= full diffusion); shows intermediate B ≈ 32 Pareto-dominates both endpoints. CASCADE will rerun these ablations to provide head-to-head numbers.
Each lit note has the same five mandatory sections:
The uniform structure makes cross-paper comparison mechanical, which means the related-work matrix in Phase 6's paper essentially writes itself from these sections.