Enhancing Diffusion Language Models with Autoregressive Post-Training Weights

1 INTRODUCTION

• The motivation is an asymmetry: dLLMs commonly inherit AR pretraining but largely discard AR post-training resources, despite the availability of capability-rich AR checkpoints.Cross-paradigm merging is nontrivial because diffusion conversion changes the model from causal next-token prediction to bidirectional denoising.Source: §1 · p. 2
• AR post-training updates transfer to diffusion models, approaching direct diffusion post-training; combining the updates can outperform both endpoints.The updates are nearly orthogonal in parameter space yet induce more aligned representation changes, and their behavioral gains are partially complementary.Source: §1 · p. 2
• A2D transfers an AR task vector to a diffusion base when no diffusion update is available, or interpolates AR-transferred and diffusion-post-trained solutions when both exist.Both operations use available checkpoints without additional trainable parameters.Source: §1 · pp. 2–3
• Across six dLLM families, A2D improves downstream performance without additional training or inference-time computation.The evaluated families include Dream, Dream-Coder, DiffuCoder, Nemotron-Labs-Diffusion, DreamReasoner, and DiffusionGemma.Source: §1 · p. 3

2.1 BACKGROUND AND NOTATIONS

• The paper defines AR and diffusion post-training vectors as parameter differences from their respective bases, Ab and Db, which share an AR initialization but differ after diffusion adaptation.AR and diffusion post-training proceed independently from their corresponding bases, raising whether an AR-branch update remains effective on the diffusion branch.Source: §2.1 · p. 3

2.2 CROSS-PARADIGM TRANSFER OF AR POST-TRAINING TO DIFFUSION

• AR task vectors substantially improve diffusion bases on math and coding, recovering a large fraction of direct diffusion post-training gains or sometimes surpassing them.The controlled comparison uses matched AR and diffusion fine-tuning data and evaluates the transfer as a scaled task vector added to the diffusion base.Source: §2.2 · p. 4, Figure 3 · p. 4
• AR and diffusion post-training vectors are nearly orthogonal in parameter space, yet induce more aligned representation changes in the diffusion model than randomized controls.The parameter cosine similarities are 0.016 for Coding and 0.009 for Math; representation changes are measured at the final-layer prediction position.Source: §2.2 · p. 4

2.3 COMPOSING AUTOREGRESSIVE AND DIFFUSION POST-TRAINING

• Interpolation between AR-transferred and diffusion-post-trained models yields high-performing solutions that outperform both endpoints in math and coding.The endpoints also have overlapping and distinct successes; the best interpolated model retains nearly all shared successes and many unique successes from each.Source: §2.3 · p. 5, Figure 4 · p. 5

2.4 A2D: CROSS-PARADIGM TRANSFER AND COMPOSITION

• A2D transfers an AR task vector to a diffusion base when no matching diffusion checkpoint exists, or interpolates AR and diffusion updates when both are available.The framework preserves the diffusion architecture and requires no additional training or inference-time hyperparameter tuning.Source: §2.4 · pp. 5–6

3 A2D ACROSS MODELS AND POST-TRAINING SETTINGS

• The evaluation spans instruction following, coding, math, medical question answering, and general reasoning, using both supervised and reinforcement-learning post-training updates.For each model family, coefficients are chosen on one anchor benchmark and held fixed on the remaining tasks.Source: §3 · p. 6

3.1 INSTRUCTION-TUNED UPDATES FOR GENERAL AND CODE MODELS

• A2D-Merge improves all 9/9 instruction-tuned baselines, while transfer and merge yield average non-anchor gains of 4.8 and 2.6 points, respectively.Transfer also shows large gains on Dream-7B MATH-500 (+19.4) and Dream-Coder BCB-Full (+6.5); coefficients selected on one anchor task generalize to remaining benchmarks.Source: §3.1 · p. 6, Table 1 · p. 7

3.2 SPECIALIZED POST-TRAINING: REASONING, MEDICAL VQA, AND CODE RL

• Across reasoning, medical SFT, and code RL, A2D-Merge improves all 9/9 post-trained baselines, with non-anchor gains averaging 4.0 points for transfer and 3.7 for merge.Reported transfer gains include +15.4 on AIME24 and +16.7 on VQA-RAD; merge gains include +10.4 on AIME25 and +6.7 on HumanEval+.Source: §3.2 · p. 7

3.3 A2D ON DUAL-MODE AR-DIFFUSION MODELS

• A2D-Merge improves or matches all 10/10 Nemotron-LD-3B benchmarks under diffusion decoding, raising the non-anchor mean from 51.0 to 54.0; the same weights raise the AR-decoding mean from 52.8 to 54.2.A2D-Transfer improves 9/10 benchmarks, while the evaluation applies AR updates only to parameters aligned with the diffusion recipient.Source: §3.3 · p. 8

4.1 UNDERSTANDING CROSS-PARADIGM TRANSFER

• A2D improves accuracy from 38.4 to 42.8 using merged-model predictions with the diffusion parent’s schedule, while the merged schedule with parent predictions reaches 42.2; combining both yields 45.0.On the parent’s intermediate states, A2D selects different positions at 5.3% of steps and commits different tokens at 3.4% of positions.Source: §4.1 · p. 8
• A2D does not systematically shift denoising toward left-to-right decoding, and the merged model closely tracks the diffusion parent on global and local AR-ness metrics.The study measures these metrics over responses up to the first EOS.Source: §4.1 · pp. 8–9
• A2D’s changed tokens concentrate at positions where the diffusion parent has relatively low confidence, while largely preserving its predictions.Source: §4.1 · p. 9
• AR-to-diffusion transfer improves the recipient, but reverse transfer can degrade performance; the authors suggest shared training lineage partly explains this asymmetry.The diffusion base descends from the AR base on which the transferred update was learned, whereas the reverse direction lacks that compatibility.Source: §4.1 · p. 9
• Transfer works broadly for downstream fine-tuning updates, but not for tested continued-pretraining vectors whose norms are 70–82× larger.The authors delimit A2D’s scope to relatively local post-training updates rather than pretraining-scale transformations.Source: §4.1 · p. 9

4.2 ABLATION STUDIES

• A2D’s full gain depends on both adding the AR update and partially removing the diffusion update, while neither component alone matches A2D-Merge.Both components individually improve over the diffusion parent.Source: §4.2 · p. 9
• A2D-Transfer depends mostly on AR updates in MLP modules, whereas A2D-Merge requires both MLP and attention modules for optimal merging performance.Source: §4.2 · p. 9

Diffusion language models

• Diffusion language models often build on pretrained AR checkpoints to reuse linguistic knowledge, while diffusion post-training faces challenges from partially corrupted states and RL likelihood estimation.Source: §5 · pp. 9–10

Autoregressive and diffusion language models

• Prior findings suggest AR and diffusion models share reusable knowledge while retaining distinct inductive biases, motivating the paper’s weight-space study of AR update transfer and composition.Source: §5 · p. 10

Model merging

• Model merging combines independently trained models in weight space without additional training, and task arithmetic treats fine-tuning updates as composable task vectors [Wortsman et al., 2022; Ilharco et al., 2022].Prior work addresses interference through conflict resolution, sparsification, and layer-wise rescaling [Yadav et al., 2023; Wang et al., 2024; Wang et al., 2025a; Yang et al., 2024b].Source: §5 · p. 10
• Prior LLM merging work focuses mainly within AR models, while Lin et al. (2026) transfers AR preference-alignment updates; this paper studies broader post-training transfer to improve already post-trained diffusion models across objectives, capabilities, and families.Source: §5 · p. 10

6 CONCLUSION

• Across diverse model families, tasks, and post-training settings, A2D improves diffusion models without additional training or inference-time computation.It transfers AR post-training updates to diffusion base models and composes AR and diffusion updates when both are available.Source: §6 · p. 10

A EXPERIMENTAL DETAILS

• Appendix A describes the evaluation procedures, merge construction, and coefficient selection.Source: A EXPERIMENTAL DETAILS · p. 17

A.1 MODELS AND THE EVALUATION PIPELINE

• The evaluation pipeline pairs each diffusion model with its AR base and post-trained checkpoints, reproduces parent-model results, and records departures from official protocols.The Nemotron-LD-8B Base has zero chat-marker embeddings, so the main evaluation uses raw prompts rather than an instruction interface that would inflate gains.Source: §A.1 · pp. 17–18
• Evaluation uses family-specific benchmarks and settings, including Dream-family harnesses, Nemotron protocols, and domain-specific DiffusionGemma fine-tuning.Nemotron transfer uses the donor’s [INST] interface; DiffusionGemma is evaluated on medical VQA tasks because no public base checkpoint is available.Source: §A.1 · pp. 17–18

A.2 DETAILS FOR MODEL MERGING

• Merging is model-family dependent: Qwen-derived models use direct parameter-wise combinations, while Nemotron and DiffusionGemma require mapped updates and protected or unmerged components.Nemotron merges protect mismatched token rows and preserve the diffusion output head; DiffusionGemma leaves its diffusion-specific adapters unmerged.Source: §A.2 · p. 19

A.3 EXPERIMENTAL DETAILS FOR SECTION 2

• The section 2 experiments fine-tune matched AR and diffusion models on math and coding data, then evaluate them zero-shot with specified templates, budgets, and scoring procedures.The fine-tuning uses 100K examples per task and one epoch; evaluation covers GSM8K, MATH-500, HumanEval+, and MBPP+.Source: §A.3 · p. 20

A.4 GPU AND TRAINING TIME

• The four section 2 fine-tuning runs take 30.8 GPU-hours in total, with each run taking 6.1–9.2 GPU-hours on four H100/H200 GPUs.Source: §A.4 · p. 20

A.5 HYPERPARAMETER SEARCH

• Each construction’s coefficient is selected on an anchor benchmark and then fixed on the other benchmarks.Nemotron-LD transfer sweeps use a 1,280-token budget on all 541 IFEval prompts; a separate comparison found this preserved the tested ranking and selected coefficient.Source: §A.5 · p. 20, Table 6 · p. 21, Table 7 · p. 21

B ADDITIONAL RESULTS

• The appendix’s additional-results section collects further experimental results.Source: B ADDITIONAL RESULTS · p. 23

B.1 FULL RESULTS FOR ANALYSES AND ABLATIONS

• A2D mainly changes low-confidence token predictions; MLPs carry more of standalone AR transfer, while attention contributes more complementary gains in merges.The parent’s decoding order is largely preserved.Source: §B.1 · p. 23, Figure 5 · p. 23, Table 14 · p. 24

B.3 FULL RESULTS OF NEMOTRON-LD-3B

• For Nemotron-LD-3B, A2D-Transfer strengthens the Base checkpoint to near or above Instruct on several benchmarks, and A2D-Merge further improves on Instruct under both decoding regimes.Source: §B.3 · p. 24

B.4 RESULTS OF NEMOTRON-LD-8B

• Instruction-donor transfer broadly improves the Nemotron-LD-8B Base, while merge gains are less consistent than at 3B and comparisons on reasoning-intensive tasks are partly confounded by shortened generations.Source: §B.4 · p. 24
• With matched explicit thinking behavior, the Nemotron-LD-8B reasoning-donor merge raises the mean score from 59.9 to 64.3 and from 60.4 to 65.6 when the generation budget doubles.Under the official budget, MATH-500 rises from 87.2 to 92.6, GPQA from 36.4 to 44.4, AIME24 from 33.3 to 46.7, and LiveCodeBench from 26.9 to 38.1.Source: §B.4 · p. 24

B.5 DIFFUSIONGEMMA WITH SLAKE POST-TRAINING

• On SLAKE, the AR donor is weaker than its diffusion counterpart, yet its task vector transfers to the diffusion base and improves the diffusion post-trained model across all three benchmarks.Source: §B.5 · p. 25

B.6 SELF-SPECULATIVE DECODING OF NEMOTRON

• Under self-speculative decoding, A2D consistently increases tokens per forward evaluation and generally improves accuracy; non-thinking merges also improve observed time per token on both benchmarks and model sizes.The reported benefits also extend to MATH-500 with a reasoning donor and thinking enabled.Source: §B.6 · p. 25

• The analysis measures concatenated parameter differences over backbone tensors using ℓ2 norms and cosine similarities, with Nemotron also including compatible mapped input-embedding rows.Output heads are excluded, as are all input embeddings for model families other than Nemotron.Source: §B.7 · pp. 25–26
• For most SFT pairs, cos(∆b, ∆p) ≥0.98, while AR and diffusion post-training vectors have low cosine similarity.DreamReasoner shows a larger change in the conversion direction and a substantially larger AR post-training update.Source: §B.7 · p. 26
• Continued-pretraining vectors are substantially larger than post-training vectors, and code continued-pretraining vectors are strongly aligned across AR and diffusion paradigms.The authors suggest the larger updates may move checkpoints beyond the local low-loss region where weight-space composition is most effective.Source: §B.7 · p. 26
• Figure 6 reports that Nemotron-LD-8B, unlike the 3B model, produces longer reasoning-like generations with thinking disabled; enabling thinking reduces the parent–merged length mismatch.Source: Figure 6 · p. 27

C.1 CORRECTION AND ERROR INTRODUCTION ALONG THE A2D DIRECTION

• Across six settings, increasing the AR contribution generally raises correction while introducing few errors near the optimal region.Some models remain robust over a broad λ range, while Dream-7B and Nemotron-LD show a clearer trade-off at larger values.Source: §C.1 · p. 29, Figure 7 · p. 29

C.2 INTERPOLATION PRESERVES COMPLEMENTARY GAINS ON RELEASED CHECKPOINTS

• On released checkpoints, diffusion parents and AR donors solve different questions, while the merged model preserves most successes from both.Source: §C.2 · p. 29, Figure 8 · p. 30

C.3 ALIGNED REPRESENTATION CHANGES ON RELEASED CHECKPOINTS

• For Dream-Coder and DiffuCoder-RL, AR and diffusion post-training updates remain nearly orthogonal in parameter space but induce substantially more aligned representation changes.The pattern also holds for DiffuCoder-RL's RL-derived updates.Source: §C.3 · p. 29, Figure 9 · p. 30

• A2D currently relies on compatible training lineage; all studied pairs share an AR family, and transfer to more distant or independently trained pairs remains unclear.Nemotron experiments show exact architectural correspondence is not required.Source: D LIMITATIONS AND FUTURE WORK · p. 31
• Observed transfer is primarily limited to relatively local post-training updates; continued-pretraining updates are larger and did not transfer effectively in these experiments.The authors suggest pretraining-scale transformations may require additional alignment or decomposition.Source: D LIMITATIONS AND FUTURE WORK · p. 31
• Future work could characterize cross-paradigm compatibility, develop more adaptive composition strategies, and study A2D as an initialization for subsequent SFT or RL.Source: D LIMITATIONS AND FUTURE WORK · p. 31