cs.AIFeb 20, 2026
SaveThink First, Diffuse Fast: Improving Diffusion Language Model Reasoning via Autoregressive Plan Conditioning
Organizations: Independent Researcher
Abstract
Diffusion large language models (dLLMs) generate text via iterative denoising but consistently underperform on multi-step reasoning. We hypothesize this gap stems from a coordination problem: AR models build coherence token-by-token, while diffusion models must coordinate all positions simultaneously. We propose plan conditioning, a training-free method that prepends a short (~100-token) natural-language plan from an AR model to the diffusion model's prompt. The plan serves as a frozen scaffold -- globally visible context that every token position can attend to from the first denoising step. On GSM8K, plan conditioning improves LLaDA-8B-Instruct from 75.6% to 87.2% (+11.6 percentage points), matching a same-size AR model (LLaMA 3.1 8B, 87.7%) despite a 6.4pp weaker baseline. On HumanEval, the gain is +12.8pp (37.2% to 50.0%), showing plans generalize to code. The same plans improve LLaMA by only +5.7pp on GSM8K and +1.3pp on HumanEval -- diffusion models benefit 2-10x more, supporting the coordination-problem hypothesis. Across 5 random seeds, plan-conditioned GSM8K accuracy has zero standard deviation, making diffusion inference highly stable. Ablations reveal the model follows plan strategy (wrong-strategy plans cause -16.3pp) but is robust to plan values (perturbed numbers: -1.1pp), and that planner quality has a sharp threshold: smaller Llama-class plans hurt (-1.6 to -6.8pp) while frontier plans provide the full lift. Attention analysis confirms the mechanism: plan tokens receive 1.8x excess attention during early denoising, declining to uniform as completion tokens solidify. Plan conditioning costs ~$0.002 per problem and adds ~2s of latency.
Figures & tables
| Format | Description | Example snippet |
|---|---|---|
| Strategy | High-level approach in 1–2 sentences | “Calculate daily production, subtract consumed, find remaining” |
| Outline | Step-by-step procedure without computing answers | “Step 1: Identify total chickens. Step 2: …” |
| Constraints | Key facts, pitfalls, expected answer form | “Daily production: 16 eggs. Pitfall: don’t double-count…” |
| Hybrid | Strategy sentence + key constraints | “Track eggs through pipeline. Key: 16/day produced, 3/day consumed…” |
Table 1: Plan format taxonomy. Each format provides different guidance density per token. Hybrid combines high-level strategy with specific numeric anchors.
Figure 1: Accuracy across benchmarks and model–condition pairs. On GSM8K, plan conditioning improves LLaDA by +11.6pp (vs. +5.7pp for LLaMA with the same plans), closing the diffusion–AR gap entirely. HumanEval shows the largest diffusion advantage: LLaDA gains +12.8pp while LLaMA gains only +1.3pp. On Countdown, both architectures start at identical baselines and benefit identically (+12.1pp).
| Benchmark | Baseline | Strategy | Outline | Constraints | Hybrid | Best |
|---|---|---|---|---|---|---|
| 128 / 256 | 128 / 256 | 128 / 256 | 128 / 256 | 128 / 256 | ||
| GSM8K | 69.0 / 75.6 | 77.7 / 85.7 | 78.2 / 84.9 | 76.8 / 86.0 | 82.0 / 87.2 | +11.6 |
| MATH500 | 27.4 / 35.8 | 30.6 / 37.4 | 34.4 / 36.6 | 30.0 / 37.6 | 32.6 / 41.8 | +6.0 |
| HumanEval | 25.0 / 37.2 | 32.3 / 50.0 | 42.1 / 48.8 | 28.0 / 36.0 | 32.9 / 48.2 | +12.8 |
| Countdown | 21.1 / 19.1 | 29.7 / 28.5 | 18.4 / 21.5 | 22.3 / 14.5 | 28.1 / 31.2 | +12.1 |
| Sudoku | 11.6 / 6.9 | 5.7 / 7.9 | 6.3 / 6.1 | 7.3 / 7.7 | 7.2 / 6.2 | +1.0 |
Table 2: LLaDA-8B accuracy (%) by plan format and generation length. Bold indicates best per row. Baseline values are at generation lengths 128/256; is computed from the 256-token baseline. Hybrid plans win on 3/5 benchmarks at gen-256; strategy wins on HumanEval and Sudoku.
Figure 2: Accuracy improvement (pp) over baseline by plan format and benchmark at generation length 256. Hybrid plans (rightmost column) dominate on 3/4 benchmarks. Sudoku (bottom row) shows near-zero or negative deltas across all formats—plans do not help spatial constraint propagation. The blue cell (Countdown–Constraints, 4.6pp) shows that constraint-only plans hurt when they lack procedural structure.
| Condition | LLaMA 3.1 8B (AR) | LLaDA-8B (Diffusion) |
|---|---|---|
| GSM8K | ||
| Bare | 82.0 | 75.6 |
| + Sonnet plan | 87.7 (+5.7) | 87.2 (+11.6) |
| + Haiku plan | 84.9 (+2.9) | 82.3 (+6.7) |
| MATH500 | ||
| Bare | 43.0 | 35.8 |
Table 3: AR vs. diffusion comparison. Accuracy (%) with per-condition lift in parentheses. On GSM8K, LLaDA benefits 2 more from Sonnet plans than LLaMA (+11.6 vs. +5.7pp). On Countdown, both architectures benefit identically (+12.1pp). On HumanEval, the diffusion advantage is largest: LLaDA gains +12.8pp while LLaMA gains only +1.3pp.
| Plan Budget | GSM8K | Countdown | ||
|---|---|---|---|---|
| Accuracy | Lift | Accuracy | Lift | |
| 0 (bare) | 75.6 | — | 19.1 | — |
| 25 tokens | 79.5 | +3.9 | 17.6 | 1.5 |
| 50 tokens | 83.0 | +7.4 | 16.8 | 2.3 |
| 100 tokens | 87.2 | +11.6 | 31.2 | +12.1 |
| 150 tokens | 88.0 | +12.4 | 39.5 | +20.4 |
Table 4: LLaDA accuracy (%) by plan token budget (hybrid format). GSM8K shows smooth saturation with diminishing returns past 100 tokens. Countdown exhibits a sharp performance threshold: plans hurt at 25–50 tokens, then jump +14.5pp from 50 100. Both benchmarks plateau by 150–200 tokens.
Figure 3: LLaDA accuracy vs. plan token budget (hybrid format). Left: GSM8K shows smooth saturation with diminishing returns past 100 tokens. Right: Countdown exhibits a sharp performance threshold—plans hurt at 25–50 tokens, then jump +14.5pp from 50 100. Dashed line marks the no-plan baseline.
| Category | Accuracy (%) | |
|---|---|---|
| No leakage (answer absent from plan) | 80.1 | 1,022 |
| False-positive leak (answer already in problem) | 83.5 | 85 |
| True leakage (answer new in plan) | 88.7 | 212 |
| Baseline (no plan) | 75.6 | 1,319 |
Table 5: Leakage decomposition for GSM8K hybrid plans ( ). “False-positive leak” denotes problems where the answer number already appears in the problem text (e.g., “20 chickens” when the answer is 20), so its presence in the plan is not informative. Even excluding all leaked problems, accuracy exceeds the baseline by +4.5pp. Maximum leakage contribution: 1.4pp out of 11.6pp (12%). Note: per-category accuracies are from the gen=128 ablation run (overall 82.0%); the qualitative conclusion—that leakage accounts for at most 12% of the lift—holds for the gen=256 run (87.2%) as well.
| Planner | GSM8K | MATH500 | Countdown | Cost/plan |
|---|---|---|---|---|
| None (baseline) | 75.6 | 35.8 | 19.1 | $0 |
| LLaDA self-plan | 74.9 ( 0.7) | — | — | $0 |
| Llama 3.2 3B | 68.8 ( 6.8) | 30.0 ( 5.8) | 16.4 ( 2.7) | $0.00005 |
| Llama 3.1 8B | 74.0 ( 1.6) | 31.6 ( 4.2) | 13.3 ( 5.8) | $0.0001 |
| Haiku 4.5 | 82.3 (+6.7) | 34.4 ( 1.4) | 24.2 (+5.1) | $0.0006 |
| Sonnet 4.5 | 87.2 (+11.6) | 41.8 (+6.0) | 31.2 (+12.1) | $0.002 |
Table 6: LLaDA accuracy (%) by planner capability. Plan quality has a sharp threshold: below Haiku-class capability, plans hurt across all benchmarks.
Figure 4: GSM8K accuracy by planner capability. There is a sharp quality cliff between Haiku (helpful, +6.7pp) and Llama 8B (marginally harmful, 1.6pp). Self-plans (LLaDA planning for itself) are indistinguishable from no plan.
| Benchmark | Rescue rate (hard) | Retention rate (easy) | Fix:Break ratio |
|---|---|---|---|
| GSM8K | 71.4% | 92.3% | 3.0:1 |
| MATH500 | 21.5% | 78.2% | 1.8:1 |
| Countdown | 28.0% | 44.9% | 2.1:1 |
Table 7: Per-difficulty analysis of hybrid plan conditioning. “Rescue rate” is the fraction of baseline-incorrect problems that plans fix; “retention rate” is the fraction of baseline-correct problems that remain correct. Plans are not a free lunch: they break 8–55% of previously correct answers, but fix even more.
| Category | Count | % of failures |
|---|---|---|
| Execution error (right plan, wrong math) | 100 | 59.2 |
| Format failure (right answer, wrong format) | 31 | 18.3 |
| Plan wrong (plan misled the model) | 27 | 16.0 |
| No answer extracted | 11 | 6.5 |
Table 8: Error taxonomy for 169 GSM8K hybrid failures. The dominant failure mode (59%) is execution error: the plan is correct but the model makes arithmetic mistakes. Zero failures were classified as “plan ignored.”
| Condition | GSM8K (%) | What it tests | |
|---|---|---|---|
| Wrong strategy | 59.3 | 16.3 | Incorrect mathematical approach |
| Mismatched plan | 71.0 | 4.6 | Plan for a different problem |
| Perturbed numbers | 74.5 | 1.1 | Correct strategy, wrong values |
| Baseline (no plan) | 75.6 | — | |
| Random tokens | 78.2 | +2.6 | Token count only |
| Shuffled plan | 80.0 | +4.4 | Vocabulary preserved |
Table 9: Plan quality spectrum on GSM8K. The model follows plan strategy (wrong strategy: 16.3pp) but is robust to plan values (perturbed numbers: 1.1pp). 61% of the improvement comes from semantic content; 23% from extra tokens; 16% from domain vocabulary. The “real plan” control in this ablation run scored 86.9% vs. 87.2% in the main sweep (Table 2 ); the 0.3pp difference reflects single-seed variance.
Figure 5: Plan quality spectrum on GSM8K. Wrong-strategy plans cause catastrophic failure ( 16.3pp), while perturbed-numbers plans are nearly neutral ( 1.1pp). The model follows the plan’s reasoning approach but computes its own values.
Figure 6: Attention from completion tokens to sequence regions across denoising steps. (a) Plan tokens receive 43% of attention at step 0 despite comprising only 24% of the sequence (dotted line = uniform baseline). By step 63, attention converges to near-uniform. (b) Excess plan attention (ratio over uniform) is 1.8 at step 0, declining smoothly to 1.0 . (c) The effect is consistent across all layers; early layers (layer 0) show the strongest absolute attention to plans.
Figure 7: Excess plan attention across plan quality conditions. (a) All conditions show elevated plan attention during early denoising, declining toward uniform. (b) Step-0 excess attention scales with plan coherence (Sonnet Llama 3B wrong strategy random) but not with downstream accuracy impact. The model reads plans indiscriminately; quality discrimination is downstream.
| Condition | GSM8K | MATH500 | Rel. FLOPs |
|---|---|---|---|
| Baseline (gen=256, steps=128) | 75.6 | 35.8 | 1.0 |
| Longer gen (gen=384, steps=192) | 78.9 (+3.3) | 34.4 ( 1.4) | 1.5 |
| More steps (gen=256, steps=256) | 79.3 (+3.7) | 34.4 ( 1.4) | 2.0 |
| Plan conditioning | 87.2 (+11.6) | 41.8 (+6.0) | 1.0 * |
Table 10: Plan conditioning vs. compute-matched controls. Doubling denoising steps or increasing generation length 50% yields modest GSM8K gains (+3–4pp) and hurts MATH500. Plan conditioning provides 3–4 more improvement at negligible additional diffusion FLOPs. * Plan generation is external; diffusion FLOPs are unchanged.
| Benchmark | Baseline | + Sonnet plan | |
|---|---|---|---|
| GSM8K | 75.51 0.15 | 88.02 0.00 | +12.5 |
| MATH500 | 35.76 0.08 | 41.52 0.56 | +5.8 |
| Countdown | 17.73 1.01 | 37.11 2.60 | +19.4 |
Table 11: Five-seed evaluation (mean s.d. across seeds). Baseline variance is remarkably low on GSM8K ( 0.15pp) and MATH500 ( 0.08pp), confirming single-seed estimates are representative. All improvements are significant ( , paired bootstrap). Plan-conditioned GSM8K has zero variance across seeds.
Figure 8: Five-seed evaluation with error bars (1 s.d.). Plan conditioning produces large, statistically significant improvements across all three benchmarks. On GSM8K, plans reduce variance to zero—the same problems are solved regardless of the random seed.
| Benchmark | LLaDA | + Sonnet Plan | Berr. BL | Berr. Text | Berr. Latent | |
|---|---|---|---|---|---|---|
| DART5 | 11.0 | 17.2 | +6.2 | 15.0 | 27.0 | 54.0 |
| ARC-Challenge | 71.3 | 75.2 | +3.9 | 87.5 | 91.0 | 81.0 |
| AIME24 | 0.0 | 3.3 | +3.3 | 1.5 | 1.5 | 14.0 |
Table 12: Plan conditioning on benchmarks from Berrayana et al. (2025) . “Berr. BL” is their LLaDA-only baseline. “Berr. Text” is their best text-space collaboration result (any direction). “Berr. Latent” is their best latent-space DDLM ARM result. Uses a trained Linear-GELU-Linear projector on 35K domain-specific samples. On ARC-C, text-space collaboration (91.0%) outperforms latent (81.0%), but on DART5 and AIME the latent projector provides dramatically higher accuracy.
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