💬 NLP

When to Plan, When to Polish: Noise Level as a Granularity Axis for Diffusion Language Models

This paper proposes Noise Dependent Granularity Control (NDGC), a single-level diffusion language model method that dynamically adjusts token grouping based on noise levels to enable early coarse structural planning and subsequent fine-grained refinement without requiring explicit hierarchical architectures or separate planners.

Original authors: Peihong Li, Yuanjie Shi, Yan Yan

Published 2026-06-23

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Peihong Li, Yuanjie Shi, Yan Yan

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Problem: The "Scattered Crumbs" Dilemma

Imagine you are trying to reconstruct a shattered vase.

Standard AI (The Old Way): Imagine the AI is given a pile of scattered crumbs. It has to guess what the vase looked like by looking at one tiny crumb at a time. At the very beginning, when the vase is most broken (high "noise"), the crumbs are so far apart that the AI can't see the shape. It just guesses, "Maybe this crumb is blue?" and "Maybe that one is red?" It ends up guessing local details without understanding the big picture. It tries to fix the vase by gluing on random pieces, often resulting in a mess where the vase repeats the same pattern over and over or falls apart.
The Goal: We want the AI to first figure out the shape of the vase (the plan), and then figure out the color and texture (the polish).

The Solution: NDGC (Noise-Dependent Granularity Control)

The authors propose a new method called NDGC. Think of this as a smart renovation crew that changes its tools based on how broken the house is.

The core idea is simple: Use the "noise level" (how broken the text is) to decide how big of a piece the AI should look at.

High Noise (The "Planning" Phase):
- The Situation: The text is very corrupted; most of it is hidden.
- The Old Way: The AI still looks at one word at a time. It sees isolated, confusing fragments.
- The NDGC Way: The AI is trained to look at chunks of words (like a whole sentence or a phrase) at once. Instead of seeing scattered crumbs, it sees readable windows of text.
- The Analogy: Instead of looking at a single brick, the AI looks at a whole wall. This helps it decide, "Okay, this wall goes on the left, and that wall goes on the right." It builds the skeleton or the map of the story early on.
Low Noise (The "Polishing" Phase):
- The Situation: The text is mostly clean; only a few words are hidden.
- The NDGC Way: Now that the "skeleton" is built, the AI switches back to looking at single words.
- The Analogy: The house is built; now the AI is just painting the walls, fixing the doorknobs, and arranging the furniture. It refines the wording.

How It Works (Without Extra Tools)

Usually, to get an AI to "plan" before it "writes," you need to build a complex system with two separate parts: one part that writes an outline, and another part that writes the story.

NDGC is clever because it does this with just one tool. It doesn't add a new "planner" robot. Instead, it teaches the same robot to change its behavior based on the noise level:

Training: The AI is taught to see groups of words when the noise is high.
Inference (Generation): When the AI is actually writing, it follows the same rule. If the noise is high, it commits to whole groups of words (the plan). If the noise is low, it commits to single words (the polish).

The Results: What Happened?

The researchers tested this on a task where the AI had to write a story following a specific, hidden order of topics (like: Newsroom → Space → School → Desert → Museum).

The Old Way (Standard AI): The AI got stuck. It would write a bunch of text about the "Newsroom," then get confused, repeat the newsroom stuff, and never actually get to the "Space" or "Desert" parts. It was like a writer who keeps rambling about the same sentence and never moves the plot forward.
The NDGC Way: The AI successfully built the "skeleton" early. It quickly established that the story starts in the newsroom, then moves to space, then school, etc. It didn't get stuck in loops. The final stories were much more organized, had fewer repetitions, and actually followed the hidden plan.

The Takeaway

The paper claims that noise level isn't just about how much text is hidden; it's a signal for how the AI should think.

High Noise = Big Picture Thinking: Look at groups of words to build the structure.
Low Noise = Detail Thinking: Look at single words to fix the grammar and style.

By aligning the training (what the AI sees) with the testing (what the AI decides), the AI learns to plan first and polish later, all without needing a separate planning system. It turns a chaotic "guessing game" into a structured "construction project."

Technical Summary: When to Plan, When to Polish

Problem Statement

Standard discrete diffusion language models (LMs) operate with a fixed tokenwise granularity throughout the entire denoising trajectory. In these models, both the training corruption (masking) and the inference commitment (revealing tokens) occur at the individual token level, regardless of the noise level.

The authors argue that this fixed granularity is a fundamental limitation for generation tasks requiring planning (e.g., long-form storytelling, structured writing).

The Issue: At high noise levels (early denoising steps), uniform tokenwise masking leaves the model with scattered, isolated word fragments ("word crumbs") rather than coherent semantic evidence. Consequently, the model is forced to make local token guesses based on weak clues rather than forming a coherent global structure (a "skeleton") early in the process.
The Gap: While hierarchical planning methods exist (e.g., "Plan and Write" systems or block-level diffusion), they require explicit planners, block-level latents, or multi-stage designs. The paper asks whether a single-level diffusion LM can inherently support early planning and late polishing by leveraging its existing noise level as a granularity cue, without adding external architectural complexity.

Methodology: Noise Dependent Granularity Control (NDGC)

The authors propose Noise Dependent Granularity Control (NDGC), a method that aligns the granularity of training exposure and inference commitment with the noise level ( $t$ ). The core intuition is: High noise = Planning (coarse groups); Low noise = Polishing (fine tokens).

1. Structured Exposure (Training)

Instead of masking tokens independently, NDGC introduces a noise-dependent span masking strategy:

Granularity Coefficient ( $s(t)$ ): A function of the noise level $r(t)$ that scales from 0 (low noise) to 1 (high noise).
Group Size ( $B(t)$ ): The target group length is calculated as $B(t) = \max(1, \text{round}(1 + s(t)(B_{\max} - 1)))$ .
Mechanism: At high noise, the model is trained on contiguous groups of tokens (spans). If a group is masked, the entire span is hidden; if exposed, the whole span is visible. This ensures that at high noise, the model sees coherent semantic blocks rather than scattered crumbs.
Marginal Preservation: The method preserves the marginal masking probability $r(t)$ for each token, ensuring the expected corruption rate remains consistent with standard diffusion, only changing the correlation of the corruption.

2. Matched Commitment (Inference)

To prevent a train-inference mismatch, the inference process mirrors the training granularity:

Grouped Commitment: At high noise steps, the sampler evaluates the confidence of entire groups (averaging the confidence of tokens within a masked group).
Selection: High-confidence groups are committed (revealed) together.
Refinement: As noise decreases, $B(t)$ shrinks, eventually returning to standard token-level commitment and refinement at low noise.

3. Alignment

The key innovation is the alignment of exposure and commitment. By using the same noise-dependent schedule $s(t)$ for both training and inference, the model learns to form coarse semantic structures early and refine wording later, effectively simulating a "coarse-to-fine" denoising process without an explicit planner.

Key Contributions

Identification of Limitation: The paper identifies that fixed token granularity in discrete diffusion prevents early structure formation, leading to reliance on local guesses rather than global planning.
NDGC Proposal: Introduction of a single-level diffusion method that uses noise level as a granularity signal, coupling structured span exposure during training with matched group commitment during inference.
Empirical Validation: Demonstration that NDGC shifts skeleton formation earlier in the denoising trajectory, improves ordered recovery of topics, and reduces degenerate outputs (repetition) compared to uniform tokenwise baselines.

Experimental Results

The authors evaluated NDGC on SYNTHETIC-V4 (a controlled benchmark with ordered latent topic skeletons) and WritingPrompts (a naturalistic story generation dataset).

SYNTHETIC-V4 (BD3LM Backbone)

Baseline Failure: Standard uniform tokenwise diffusion failed significantly on this task, with only 27.8% final topic coverage and 99.7% bad output rate (driven by repetition and lack of diversity).
NDGC Performance: NDGC ( $B_{\max}=16$ ) achieved 84.2% final topic coverage, 79.8% order accuracy, and reduced bad outputs to 3.7%.
Early Formation: Crucially, NDGC showed significantly higher Early Recovery (79.1%) and Early Order (77.0%) compared to the baseline (28.7% and 27.5%), proving that structure is formed earlier, not just repaired at the end.
Ablations:
- Structured Commitment Only: Improved coverage but failed to fix bad outputs (89.0%), indicating inference heuristics alone are insufficient.
- Structured Exposure Only: Improved health but failed to achieve high exact skeleton matches, indicating a train-inference mismatch.
- Tokenwise Early: Even with structured training, forcing token-level commitment at high noise delayed skeleton formation.

Cross-Backbone and Naturalistic Checks

MDLM & SEDD: NDGC improved skeleton recovery and maintained healthy outputs on other backbones (MDLM, SEDD), though the magnitude of gain varied.
WritingPrompts: On naturalistic data without gold skeletons, NDGC improved output health (bad output dropped from 22.8% to 10.9%) and reference-aligned segment similarity (RASC-best), while reducing repetition.

Significance and Claims

The paper claims that noise level can serve as a semantic granularity axis for single-level diffusion language models.

Mechanism: By aligning training exposure and inference commitment, NDGC enables a model to "plan" (commit to coherent spans) when evidence is scarce (high noise) and "polish" (commit to tokens) when evidence is abundant (low noise).
Efficiency: This approach achieves planning-like behavior without requiring explicit planners, hierarchical architectures, or multi-stage pipelines.
Modesty: The authors acknowledge that their strongest evidence comes from the controlled SYNTHETIC-V4 setting. While WritingPrompts supports the findings regarding output health and coherence, it does not provide direct evidence of latent skeleton recovery. They note that future work could explore learned semantic boundaries and longer documents.

In summary, the paper argues that the "scattered crumbs" problem in standard diffusion is solvable by dynamically adjusting the granularity of the denoising process, allowing a single-level model to naturally transition from structural planning to lexical refinement.