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LLaDA MoE v2: Scaling Mixture-of-Experts Diffusion Language Models

Fengqi Zhu, Shaoxuan Xu, Jingyang Ou, Zebin You, Yipeng Xing, Huabin Liu, Xiaolu Zhang, Jun Zhou, Zhenzhong Lan, Yankai Lin, Wayne Xin Zhao, Jianguo Li, Chongxuan Li, Ji-Rong Wen

arXiv:2608.03457v1cs.AI

TL;DR

Scaling behavior for MoE diffusion language models remains poorly characterized, and prior dLLM scaling studies have mainly focused on dense architectures. This paper systematically studies optimization, compute allocation, and architecture scaling, then reports that after SFT alone LLaDA MoE v2 outperforms SDAR Chat on seven of eight reasoning and coding benchmarks.

  • Problem

    Scaling behavior for MoE dLLMs remains poorly characterized, with prior dLLM scaling studies focused mainly on dense architectures and MoE allocation behavior uncharacterized.

    Source: §1 · p. 1, §3.2 · p. 5

  • Method

    The paper systematically characterizes compute-dependent optimization, model–data allocation, and expert-architecture choices, then applies the findings to train LLaDA MoE v2 from scratch.

    Source: §1 · p. 2

  • Results

    7 of 8 reasoning and coding benchmarks: after SFT alone, LLaDA MoE v2 outperforms SDAR Chat and remains competitive with Qwen3 across multiple benchmarks.

    Source: §1 · p. 2, §6 · p. 10

  • Takeaways & Limitations

    The findings provide practical design principles for scaling MoE dLLMs, with AR trends serving as useful priors that require dLLM-specific calibration.

    Source: §1 · p. 2, §6 · p. 10

    The experiments vary scaling dimensions separately and therefore do not capture their interactions.

    Source: §6 · p. 10

Abstract

from arXiv · show

Diffusion language models (dLLMs) offer an alternative to autoregressive (AR) language modeling, yet the scaling behavior of Mixture-of-Experts (MoE) dLLMs remains poorly understood. We systematically characterize how optimization hyperparameters, compute allocation, and architecture scale for MoE dLLMs, identifying quantitative differences from scaling trends previously reported for AR models. Specifically, for optimization, the optimal nominal batch size grows faster, while the optimal learning rate decays more rapidly with compute. For model--data allocation, IsoFLOP analysis reveals a slight data-side tilt: the optimal token budget grows faster than activated model-side computation. For MoE architecture, larger scales increasingly favor larger expert pools at fixed activated capacity, while moderate expert granularity remains consistently effective and the preferred fraction of activated capacity assigned to shared experts remains stable across scales. Guided by these findings, we train LLaDA MoE v2, a 30B-A3B dLLM, from scratch on 23.5T tokens. With approximately 65\% as many pretraining tokens as Qwen3, LLaDA MoE v2 approaches Qwen3 on several knowledge, reasoning, and coding benchmarks. After supervised fine-tuning alone, it outperforms SDAR Chat on seven of eight reasoning and coding benchmarks and remains close to Qwen3 on several tasks. These results establish practical scaling laws and design principles for MoE dLLMs.

1 INTRODUCTION

The introduction frames MoE dLLM scaling as an open, dLLM-specific problem and presents systematic scaling studies and LLaDA MoE v2 as practical validation.

Introduction

  • MoE dLLM scaling remains undercharacterized: prior dLLM scaling studies focused on dense models, while denoising, masked-position supervision, and corrupted-sequence conditioning distinguish dLLMs from AR models.Source: §1 · pp. 1–2
  • Across scales, lower activation ratios become favorable, G=8–16 expert granularity remains robust, and the shared-expert ratio stays at S=33.3%.Source: §1 · p. 2
  • The study systematically examines compute-scale optimization, allocation between activated model computation and training tokens, and MoE routing, expert granularity, and shared capacity.It asks how optimal batch size and learning rate change with compute, how a fixed compute budget should be split, and how activated capacity should be decomposed.Source: §1 · p. 2
  • Trained from scratch on 23.5T tokens, LLaDA MoE v2 approaches Qwen3 30B-A3B with approximately 65% as many tokens and beats SDAR Chat 30B-A3B on 7/8 benchmarks after SFT.It remains competitive with Qwen3 across multiple benchmarks despite Qwen3’s additional RL stage, and matches a prior MoE dLLM developed without this scaling guidance at a fraction of its training compute. It also matches or exceeds 7B-A1B at substantially lower compute.Source: §1 · p. 2

2 PRELIMINARIES

The preliminaries define masked diffusion language models as iterative denoisers and introduce the MoE architecture and compute framework used to study scaling.

2.1 DIFFUSION LANGUAGE MODELS

  • Masked diffusion independently replaces each token with [MASK] at noise level t, then trains a bidirectional Transformer to recover clean tokens and generates by iterative denoising.With uniformly sampled noise levels, the denoising objective upper-bounds the data's negative log-likelihood; inference begins from a fully masked sequence.Source: §2.1 · pp. 2–3

2.2 MIXTURE-OF-EXPERTS TRANSFORMERS AND SCALING LAWS

  • MoE Transformers separate total parameter capacity from per-token computation, while scaling laws guide compute-dependent choices using power-law fits and fixed-compute IsoFLOP analysis.Each token activates top-na routed experts plus one shared expert; the architecture is described by activation ratio A, granularity G, and shared-expert ratio S. For MoE scaling, compute is C = MD, where M is activated non-embedding training FLOPs per token and D is training tokens.Source: §2.2 · p. 3

3 SCALING LAWS FOR MOE DLLMS

The section develops compute-dependent optimization, model–data allocation, and MoE architecture scaling laws for dLLMs. Its findings favor larger nominal batches and faster learning-rate decay at high compute, a slight data-side allocation tilt, and sparser activation at larger scales while moderate granularity and shared capacity remain robust.

3.1 SCALING LAW FOR HYPERPARAMETERS

  • At 1020 FLOPs, the fitted dLLM law predicts a 3.43M-token batch versus 1.02M for DeepSeek LLM, while learning rates are 8.27 × 10−4 versus 9.86 × 10−4.The dLLM fit has steeper batch-size scaling and faster learning-rate decay than the AR reference; at 6 × 1020 FLOPs its recommendation lies near the best observed configuration.Source: Figure 1 · p. 4, §3.1 · p. 4, Figure 2 · p. 4

3.2 SCALING LAW FOR COMPUTE ALLOCATION

  • The fitted allocation exponents are 0.475 for activated model-side computation and 0.525 for training tokens, so optimal token budgets grow slightly faster.The resulting rule favors spending relatively more marginal compute on additional training tokens than on increasing activated FLOPs per token.Source: Figure 3 · p. 5, §3.2 · pp. 5–6

3.3 SCALING LAW FOR MOE ARCHITECTURE

  • At fixed activated model-side compute, lower activation ratios generally reduce loss, with greater benefit at larger scales; the second-lowest ratio slightly wins at the smallest budgets.The authors suggest larger scales can better optimize the larger routed expert pool exposed by sparser activation.Source: §3.3 · pp. 6–7, Figure 4 · p. 6
  • Expert granularity shows no monotonic scale trend, and G = 8 to G = 16 is a robust range across the sweep.This reflects a trade-off between routing diversity and per-expert capacity; the exact optimum does not systematically vary with compute.Source: Figure 4 · p. 6, §3.3 · p. 7
  • Across compute scales, shared-expert loss curves reach their minima at S = 33.3%, supporting one unit of shared activated capacity per two routed units.Unlike a fixed shared component, this rule scales shared capacity proportionally with the activated model budget.Source: Figure 4 · p. 6, §3.3 · p. 7

4 TRAINING LARGE-SCALE MOE DLLMS

Guided by scaling laws, the authors train LLaDA MoE v2, a 30B-A3B diffusion language model, from scratch on 23.5T tokens. It achieves the highest average among evaluated dLLMs across 15 benchmarks and shows strong reasoning and coding performance after supervised fine-tuning alone.

4 TRAINING LARGE-SCALE MOE DLLMS

  • The 30B-A3B model has 3B active parameters per token and uses 128 routed experts with top-8 routing plus one shared expert, yielding 9.09% activated capacity and a 33.3% shared-expert fraction.Its configuration is (A, G, S) = (9.09%, 8, 33.3%), with shared-expert width 4d_expert.Source: §4 · p. 7
  • Training proceeds through five stages: 10T tokens each in Stages 1 and 2, 2T-token annealing in Stage 3, 500B tokens after extending context from 4K to 32K in Stage 4, and 1T-token long-context annealing in Stage 5.Stage 4 also increases the RoPE base from 10,000 to 500,000; Stage 5 yields the final pretrained base model.Source: §4 · p. 7

4.1 BENCHMARK RESULTS

  • Across 15 benchmarks, LLaDA MoE v2 achieves the highest evaluated dLLM average (58.60), beating SDAR Sci by 3.78 points and remaining close to Qwen3 on several reasoning and coding benchmarks.It was trained from scratch on 23.5T tokens, 65% of Qwen3’s 36T; its gaps to Qwen3 are larger on CEval, CMMLU, and some coding tasks.Source: §4.1 · p. 7, Table 3 · p. 8
  • At approximately 50% of LLaDA MoE 7B-A1B’s training FLOPs, LLaDA MoE v2 surpasses it on MMLU, GSM8K, and KorBench, and does so on HellaSwag with less than 10%.The comparison uses the scaling-law-guided 30B-A3B model and the 7B-A1B model trained without scaling-law guidance.Source: §4.1 · p. 8, Figure 5 · p. 9

4.2 SUPERVISED FINE-TUNING

  • For SFT, the model trains for three epochs on 7M instruction–response examples, masking only responses; the authors do not apply reinforcement learning afterward.They use batch size 512 sequences and peak learning rate 5.0 × 10−6, with linear warmup over the first 8% of steps.Source: §4.2 · p. 9
  • After SFT alone, LLaDA MoE v2 beats SDAR Chat on all four reasoning and three of four code benchmarks, stays close to Qwen3 (Yang et al., 2025) on AIME, MBPP, and LiveCodeBench, and surpasses it on MultiPL-E.The model uses fewer pretraining tokens than Qwen3 and receives no additional reinforcement learning.Source: Table 4 · p. 8, §4.2 · p. 9

5 RELATED WORK

Related work establishes dLLMs as an emerging alternative to autoregressive models, while MoE dLLM scaling remains largely uncharacterized. The paper situates its study at the intersection of these gaps.

5 RELATED WORK

  • Masked discrete dLLMs can generate multiple tokens per denoising step; scaling studies remain mostly dense, while models have been trained from scratch or adapted from pretrained AR models (Nie et al., 2025; Ni et al., 2025b; von R¨utte et al., 2026).The literature also identifies masked discrete diffusion as a potential alternative to AR models (Arriola et al., 2025; Wei et al., 2025; Chen et al., 2026; Cheng et al., 2026b).Source: §5 · p. 9
  • MoE architectures increase capacity without proportional computation by selectively activating fine-grained experts, but MoE dLLMs largely inherit AR design choices and lack characterized scaling behavior (Shazeer et al., 2017; Lepikhin et al., 2020; Fedus et al., 2022).Prior work applies MoE to dLLMs (Zhu et al., 2025; Feng et al., 2026), but leaves optimization, compute allocation, and expert architecture scaling largely uncharacterized.Source: §5 · p. 9

6 CONCLUSION · A SCALING LAWS FOR MOE DLLMS

The conclusion presents scaling-law-guided design as practical for MoE dLLMs: LLaDA MoE v2 approaches Qwen3 on several benchmarks with fewer pretraining tokens, and SFT alone outperforms SDAR Chat on seven of eight reasoning and coding tasks.

6 CONCLUSION

  • LLaDA MoE v2 approaches Qwen3 on several benchmarks with fewer pretraining tokens, while SFT alone produces an instruct model that outperforms SDAR Chat on seven of eight reasoning and coding tasks.The SFT result is achieved without reinforcement learning.Source: §6 · p. 10
  • The study characterizes scaling in optimization hyperparameters, model–data allocation, and expert architecture for MoE dLLMs.These dimensions provide the basis for the paper’s scaling-law design principles.Source: §6 · p. 10
  • Autoregressive scaling trends provide useful priors for MoE dLLMs but require dLLM-specific calibration.Source: §6 · p. 10
  • The resulting design principles guide the from-scratch training of LLaDA MoE v2 30B-A3B.Source: §6 · p. 10
  • The experiments vary scaling dimensions separately and therefore do not capture interactions among them.Source: §6 · p. 10
  • Despite that limitation, the large-scale results demonstrate the practical value of scaling-law-guided MoE dLLM design.Source: §6 · p. 10

A.1 COMPUTE ACCOUNTING

The accounting distinguishes total and activated model parameters from non-embedding quantities, and defines activated compute per token and over training. It specifies how routed and shared experts, embeddings, and nominal masked and visible tokens contribute.

A.1 COMPUTE ACCOUNTING

  • The architecture has one shared expert per MoE layer, with shared capacity ns=dshare/dexpert measured in units of one routed expert.With SwiGLU, the shared expert has 3nsdmodeldexpert parameters.Source: §A.1 · p. 16
  • Total and activated non-embedding parameter counts differ in routed capacity: total counts all ne experts, while activated counts the na experts selected per token, plus shared capacity.The router term scores all ne experts in both counts. Input embeddings and the separate LM head are included in reported total or activated parameter counts, but excluded from non-embedding quantities.Source: §A.1 · p. 16
  • Activated non-embedding FLOPs per token count one multiply–accumulate as two FLOPs and approximate backward-pass cost as twice forward-pass cost.The accounting includes attention projections and sequence-level attention operations, routing, selected routed experts, and the shared expert; it omits embeddings, LM head, normalization, nonlinearities, and attention softmax. All layers share the same architecture, so per-layer FLOPs are multiplied by nlayer.Source: §A.1 · p. 16
  • Training compute uses D nominal tokens, including masked and visible positions, which incur equal Transformer computation despite differing numbers of supervised targets.The sampled corruption level changes the number of supervised prediction targets, not accounted FLOPs.Source: §A.1 · p. 16

A.2 MOE IMPLEMENTATION · A.3 HYPERPARAMETER SCALING

The scaling experiments use a token-routed MoE Transformer with shared and routed expert pathways, trained with fixed router-regularization coefficients. Hyperparameter scaling is assessed by jointly searching batch size and learning rate, then fitting scaling laws to near-optimal runs.

A.2 MOE IMPLEMENTATION

  • Across scaling experiments, each MoE Transformer layer pairs grouped-query attention with a SwiGLU feed-forward block containing routed experts and one shared expert, except some architecture configurations omit the shared expert.The architecture exceptions occur in the architecture experiments.Source: §A.2 · p. 16
  • Routing is performed independently for each token at every layer: a linear router maps its representation to softmax scores, from which the na largest scores are selected and renormalized.The supplied passages do not specify the renormalization formula.Source: §A.2 · pp. 16–17
  • The shared and routed expert outputs are combined as Eshare(h) + λEroute(h); routed-only shared-expert-ratio configurations omit the shared term and use no scaling factor.Source: §A.2 · p. 17
  • For configurations with shared experts, λ is estimated at initialization by matching expected shared and routed pathway output norms under equal-norm, pairwise-orthogonal expert-output assumptions.The shared expert is treated as ns expert-width units; router-logit expectations are approximated by Monte Carlo sampling for each shared-expert configuration, following Liu et al. (2025).Source: §A.2 · p. 17
  • Router training adds load-balancing and router z-loss terms directly to the denoising objective, with coefficients fixed at αaux = 0.01 and αz = 0.001 across scaling and architecture sweeps.The settings follow Fedus et al. (2022), Shazeer et al. (2017), and Zoph et al. (2022).Source: §A.2 · p. 17

A.3 HYPERPARAMETER SCALING

  • Hyperparameter scaling covers 158M, 1B, and 3.6B models at compute budgets from 10^18 to 3×10^20 FLOPs, using the same data, 4096-token sequences, and AdamW.AdamW uses (β1, β2) = (0.9, 0.95) and weight decay 0.1; the learning rate warms up for 2,000 steps, stays at peak until the final 10% of compute, then cosine-decays to 0.1η.Source: §A.3 · p. 17
  • At each compute setting, global nominal token batch size B and peak learning rate η are searched jointly while architecture and training-token budget are held fixed.Table 5 is described as summarizing architectures, compute budgets, and search grids, but its values are not included in the supplied passages.Source: §A.3 · p. 17
  • Scaling laws use log–log linear regressions of batch size and learning rate against compute, fit to all configurations within 0.25% of the minimum final-training loss at each budget.Run loss is the average over the final 0.5% of allocated training FLOPs; near-optimal configurations follow Bi et al. (2024).Source: §A.3 · p. 17

A.4 COMPUTE ALLOCATION SCALING

The section describes IsoFLOP sweeps used to estimate compute-allocation scaling laws, from controlled training runs to selecting and fitting loss-minimizing allocations.

A.4 COMPUTE ALLOCATION SCALING

  • Across 10^17–10^20 FLOPs, the IsoFLOP sweeps use the same pretraining data, denoising objective, and optimizer as Appendix A.3, with batch size and peak learning rate set by fitted scaling laws.Warmup is Twarm = max(0.01T, 100) steps; the peak rate is maintained through the final 10% of training, then cosine-decayed to 10% of peak.Source: §A.4 · pp. 17–18
  • For each compute budget, the study evaluates MoE allocations by activated non-embedding FLOPs per token M and assigns each a training-token budget D = C/M.The allocation with the lowest loss at each budget is selected as the empirical optimum.Source: §A.4 · p. 18
  • Log–log linear regression fits the selected model-side optima, and D∗(C) = C/M∗(C) yields the corresponding data-side frontier and final allocation scaling laws.Source: §A.4 · p. 18

A.5 MOE ARCHITECTURE SCALING · B TRAINING LARGE-SCALE MOE DLLMS

The section describes controlled MoE architecture sweeps at five compute budgets, preserving activated model-side computation while varying one architectural dimension at a time. Candidate selection uses final-training loss, and Table 6 is identified as the architecture of LLaDA MoE v2 30B-A3B.

A.5 MOE ARCHITECTURE SCALING

  • At five reference compute budgets, each architecture candidate is trained for 3D*(C) nominal tokens (about 3C FLOPs) with batch size and peak learning rate set for the actual training budget.The Transformer backbone is fixed, and one architecture dimension is varied at a time while the other two are held as closely as discrete configurations allow.Source: §A.5 · p. 18
  • In the activation-ratio sweep, decreasing A increases total parameter count while leaving activated expert computation per token unchanged.The sweep fixes the backbone, na, ns, and dexpert and varies only routed-expert count ne, preserving the activated model-side budget apart from negligible router contribution.Source: §A.5 · p. 18
  • The expert-granularity sweep varies dexpert and scales expert counts inversely, preserving A, S, and routed and shared activated widths.The shared widths are nadexpert and nsdexpert.Source: §A.5 · pp. 18–19
  • Table 6 presents the architecture of LLaDA MoE v2 30B-A3B.Source: Table 6 · p. 19
  • The shared-expert-ratio sweep redistributes fixed activated expert width between shared and routed pathways, with only negligible drift in A.It fixes ne and dexpert while varying ns and na; the drift does not affect the controlled comparison.Source: §A.5 · p. 19
  • At each reference budget, the selected candidate for each architectural dimension has the lowest loss, defined as average training loss over the final 0.5% of allocated training FLOPs.This follows the loss definition used in Appendix A.3.Source: §A.5 · p. 19

B.1 MODEL ARCHITECTURE · B.2 PRETRAINING · B.3 SUPERVISED FINE-TUNING

LLaDA MoE v2 is a 30B-A3B diffusion language model with a 128-expert MoE architecture, pretrained from scratch on 23.5T tokens and then supervised fine-tuned on 7M instruction–response examples. Its training uses a five-stage pretraining schedule followed by response-only denoising during SFT.

B.1 MODEL ARCHITECTURE

  • The model has 32 Transformer layers, hidden size 3072, 32 query heads, 4 key-value heads, a 157,184-token vocabulary, and MoE feed-forward blocks throughout.Its routing rule, routed/shared expert-output combination, and auxiliary objectives follow Appendix A.2; detailed architecture is reported in Table 6.Source: §B.1 · p. 19
  • The architecture activates 8 of 128 routed experts per token alongside one shared expert, yielding activated capacity A = 9.09% and shared-expert fraction S = 33.3%.With G = 8, each routed expert has width d_model/4 and the shared expert has width d_model.Source: §B.1 · p. 19

B.2 PRETRAINING

  • 23.5T nominal tokens are used to pretrain LLaDA MoE v2 from scratch on curated, high-quality web text with the denoising objective.The preprocessing pipeline removes boilerplate and malformed or low-quality documents, deduplicates repeated content, and filters harmful material.Source: §B.2 · p. 19
  • The five-stage schedule uses separate 10T-token samples in Stages 1–2, a 2T-token two-epoch annealing phase, and long-form data up to 32K tokens in Stages 4–5.Stage 2 slightly increases the weight of mathematical reasoning and code data; its 2T tokens come from a curated 1T-token corpus.Source: §B.2 · p. 19, Table 7 · p. 20
  • Pretraining uses BF16 AdamW, a 33,554,432-token nominal batch, stage-specific learning-rate schedules, and a RoPE-base increase from 10,000 to 500,000.Peak learning rates for Stages 1–5 are 1.5×10−4, 1.0×10−4, 5.0×10−5, 1.0×10−5, and 7.0×10−6; AdamW uses (β1, β2) = (0.9, 0.95) and weight decay 0.1 (Loshchilov & Hutter, 2017). The RoPE change extends context length from 4K to 32K (Xiong et al., 2024).Source: §B.2 · pp. 19–20
  • The full pretraining run consumes approximately 460,000 NVIDIA B200 GPU hours.The context length is extended from 4K to 32K at the Stage 3-to-4 transition (Xiong et al., 2024).Source: §B.2 · pp. 19–20

B.3 SUPERVISED FINE-TUNING

  • SFT fine-tunes the final pretrained checkpoint for three epochs on 7M instruction–response examples, primarily single-turn math reasoning and code generation, packed into non-overlapping 8K-token sequences.Examples are cleaned, deduplicated, filtered for harmful material, and formatted with a unified conversation template.Source: §B.3 · p. 20
  • SFT corrupts and denoises response tokens only, keeps prompts as conditioning context, retains both MoE auxiliary losses, and uses the final checkpoint without reinforcement learning.All parameters are updated with AdamW, gradient clipping, and a cosine learning-rate schedule; the load-balancing and router z-loss coefficients remain 0.01 and 0.001.Source: §B.3 · p. 20

B.4 EVALUATION · C M ∗(C) 3D∗(C) B η

The evaluation covers general, mathematical-reasoning, and code-generation benchmarks, using task-specific scoring and generation procedures. The supplied sweep tables describe compute-allocation and MoE architecture configurations, not benchmark outcomes.

B.4 EVALUATION

  • LLaDA MoE v2 is evaluated on general, mathematical-reasoning, and code-generation benchmarks.The suite includes MMLU, MMLU-Pro, CEval, CMMLU, HellaSwag, KorBench; GSM8K, MATH, OlympiadBench; and CRUXEval, MBPP, MultiPL-E, HumanEval, LiveCodeBench, BigCodeBench.Source: §B.4 · p. 20
  • Base-model results use conditional likelihood for multiple-choice tasks and conditional generation for the rest; SFT results use conditional generation throughout.Results are preferentially taken from models’ official publications, with unified-configuration scores used when benchmark results are unavailable.Source: §B.4 · p. 20
  • For five multiple-choice benchmarks, accuracy is based on the candidate answer with the highest conditional likelihood.AR likelihood uses left-to-right factorization; LLaDA MoE v2 follows protocols used in SMDM, LLaDA, and previous LLaDA MoE (Nie et al., 2025; 2026b; Zhu et al., 2025), while SDAR uses Block Diffusion’s method (Arriola et al., 2025).Source: §B.4 · p. 20
  • For conditional-generation tasks, models complete benchmark prompts using native generation, with code executed against tests and math answers checked for equivalence.Source: §B.4 · p. 21
  • Instruct models use conditional generation with a 1,024-token limit, raised to 4,096 for MATH, OlympiadBench, AIME 2024, and AIME 2025.LLaDA MoE v2 uses semi-autoregressive sampling with block size 64; SDAR uses recommended block-diffusion decoding with block size 4, and both set sampling steps to generation length (Nie et al., 2026b; Cheng et al., 2026a).Source: §B.4 · p. 21
  • Compute-allocation sweep tables specify candidate architectures and budgets, including model scale, training-token budget, nominal batch size, and peak learning rate.The architecture configurations use fitted allocation targets; candidates train for 3D∗(C) nominal tokens, approximately 3C FLOPs, with batch size and learning rate evaluated at 3C.Source: Table 8 · p. 21, Table 9 · p. 22, Table 10 · p. 24

C M ∗(C) 3D∗(C) B η

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