• “”“DiffusionLLM: Masked Discrete Diffusion for Parallel Text Generation
• ══════════════════════════════════════════════════════════════════
• 核心数据结构
• ══════════════════════════════════════════════════════════════════
• ══════════════════════════════════════════════════════════════════
• 噪声调度器
• ══════════════════════════════════════════════════════════════════
• ══════════════════════════════════════════════════════════════════
• 掩码扩散语言模型
• ══════════════════════════════════════════════════════════════════

§“”“
DiffusionLLM: Masked Discrete Diffusion for Parallel Text Generation

深度学习方向：扩散语言模型 — 打破自回归瓶颈（2026-07-05）

热点信号来源：

• DeepMind Blog: DiffusionGemma — 4x faster text generation (2026-06-10)
• 背景：GPT自回归逐token生成 → O(n²)注意力 → 推理慢
• 创新：扩散模型并行生成所有token → 迭代精炼 → 4x加速

核心原理：
▸ 前向扩散：逐步mask原始token序列（离散扩散/MDLM/D3PM）
▸ 反向去噪：一次预测所有mask位置 → 迭代精炼 → 10~256步收敛
▸ 并行解码：每步所有位置同时预测，无需KV-cache
▸ 天然支持：填词(mask-and-fill)、编辑、可控生成

论文关联技术：

• D3PM (Austin et al. 2021): 离散扩散概率模型
• MDLM (Sahoo et al. 2024): 掩码扩散语言模型 (Apple)
• Diffusion-LM (Li et al. 2022): 连续扩散+embedding映射
• LLaDA (Nie et al. 2024): 大规模掩码扩散LLM (媲美LLaMA3 8B)
• DiffusionGemma (DeepMind 2026): 生产级4x加速推理

独立运行: python diffusion_llm.py
测试覆盖: 6个单元测试 + 端到端扩散生成demo + 速度对比
“”“

import math
import random
import time
from dataclasses import dataclass, field
from typing import List, Tuple, Dict, Optional, Callable
from collections import Counter

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§核心数据结构

§══════════════════════════════════════════════════════════════════

@dataclass
class DiffusionConfig:
“”“扩散语言模型超参数”““
# 词汇
vocab_size: int = 256 # 词表大小
special_tokens: Dict[str, int] = field(default_factory=lambda: {
“<PAD>”: 0,
“<MASK>”: 1,
“<BOS>”: 2,
“<EOS>”: 3,
})

# 扩散过程
max_seq_len: int = 64            # 最大序列长度
num_timesteps: int = 100         # T: 扩散总步数（论文: 128~1024）
num_sampling_steps: int = 32     # 推理去噪步数（越少越快，越粗糙）
mask_id: int = 1                 # <MASK> token ID

# 模型
hidden_dim: int = 128            # 隐藏维度
num_layers: int = 2              # Transformer层数（模拟）

# 噪声调度
schedule_type: str = "cosine"    # cosine / linear / sqrt
# mask概率: 从p_min线性增加到p_max
mask_prob_min: float = 0.0
mask_prob_max: float = 1.0

# 训练
learning_rate: float = 0.001
grad_clip: float = 1.0

# 温度
sampling_temperature: float = 0.8

@dataclass
class DiffusionStep:
“”“单个扩散步的状态”““
t: int # 当前时间步
tokens: List[int] # 当前token序列
masked_positions: List[int] # 被mask的位置索引
confidence: List[float] # 每个位置的预测置信度

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§噪声调度器

§══════════════════════════════════════════════════════════════════

class NoiseScheduler:
“”“
离散扩散噪声调度器
控制每个时间步t的mask概率 α_t（即保留原始token的概率）

三种调度策略：
- cosine: α_t = cos(π·t / (2·T)) ，平滑，论文推荐
- linear: α_t = 1 - t/T         ，最简单
- sqrt:   α_t = sqrt(1 - t/T)    ，两端温和
"""

def __init__(self, config: DiffusionConfig):
    self.T = config.num_timesteps
    self.schedule_type = config.schedule_type
    self._alphas: List[float] = []
    self._build_schedule()

def _build_schedule(self):
    """预计算所有时间步的α值"""
    T = self.T
    self._alphas = []
    for t in range(T + 1):
        ratio = t / max(T, 1)
        if self.schedule_type == "cosine":
            alpha = math.cos(ratio * math.pi / 2)
        elif self.schedule_type == "sqrt":
            alpha = math.sqrt(max(0, 1 - ratio))
        else:  # linear
            alpha = 1.0 - ratio
        # 确保在 [0, 1] 范围内
        self._alphas.append(max(0.0, min(1.0, alpha)))

def alpha(self, t: int) -> float:
    """返回时间步t的保留概率 α_t"""
    t = max(0, min(t, self.T))
    return self._alphas[t]

def alpha_bar(self, t: int) -> float:
    """
    累积保留概率 ᾱ_t = Π_{s=0}^{t} α_s
    表示从原始token经过t步扩散后仍被保留的概率
    在mask扩散中，累积mask概率 = 1 - ᾱ_t
    """
    t = max(0, min(t, self.T))
    product = 1.0
    for s in range(t + 1):
        product *= self._alphas[s]
    return product

def get_sampling_steps(self, num_steps: int) -> List[int]:
    """
    等间距采样时间步用于推理去噪
    例如 T=100, num_steps=25 → [0, 4, 8, ..., 96, 100]
    """
    if num_steps >= self.T:
        return list(range(self.T + 1))
    # 均匀采样
    step = self.T / num_steps
    steps = [int(i * step) for i in range(num_steps + 1)]
    steps[-1] = self.T  # 确保最后一步=T
    return steps

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§掩码扩散语言模型

§══════════════════════════════════════════════════════════════════

class MaskedDiffusionModel:
“”“
模拟掩码扩散语言模型（去噪网络 p_θ(x_{t-1} | x_t)）

核心任务：给定一个部分被mask的序列x_t，预测所有被mask位置的原始token
这就是BERT-style预训练的思想，也是扩散LLM的核心

真实场景：
- 使用Transformer Encoder（类似BERT/BART）
- 输入: token embedding + positional embedding + timestep embedding
- 输出: 每个位置的词表logits
"""

def __init__(self, config: DiffusionConfig, seed: int = 42):
    self.config = config
    random.seed(seed)
    d = config.hidden_dim
    v = config.vocab_size
    T = config.num_timesteps

    # Token embedding W_e ∈ R^{V × D}
    self.W_embed = [[random.gauss(0, 0.02) for_  in range(d)] for _ in range(v)]
    # Positional embedding W_p ∈ R^{L × D}
    self.W_pos = [[random.gauss(0, 0.02) for_  in range(d)]
                  for  _in range(config.max_seq_len)]
    # Timestep embedding W_t ∈ R^{T+1 × D}
    self.W_time = [[random.gauss(0, 0.02) for_  in range(d)]
                   for _ in range(T + 1)]
    # 输出投影 W_out ∈ R^{D × V}
    self.W_out = [[random.gauss(0, 0.02) for_  in range(v)] for _ in range(d)]

    self._step = 0

def _get_embedding(self, tokens: List[int], t: int) -> List[List[float]]:
    """组合token + position + timestep embedding"""
    d = self.config.hidden_dim
    L = len(tokens)
    time_emb = self.W_time[min(t, len(self.W_time) - 1)]

    embeddings = []
    for i, tok in enumerate(tokens):
        tok = max(0, min(tok, len(self.W_embed) - 1))
        pos = min(i, len(self.W_pos) - 1)
        tok_emb = self.W_embed[tok]

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