拆解Sora的DiT与时空patch架构

# DiT自适应层归一化(adaLN)条件注入import numpy as np def layer_norm(x, eps=1e-5):    mean = x.mean(axis=-1, keepdims=True)    std = x.std(axis=-1, keepdims=True)    return (x - mean) / (std + eps) def adaLN_modulate(x, cond_embed, d_model):    W_mlp = np.random.randn(d_model, d_model * 2) * 0.02    params = cond_embed @ W_mlp    gamma = params[..., :d_model]    beta = params[..., d_model:]    x_norm = layer_norm(x)    x_modulated = (1 + gamma) * x_norm + beta    return x_modulated d_model = 768seq_len = 256x = np.random.randn(2, seq_len, d_model)t_embed = np.random.randn(2, d_model)x_mod = adaLN_modulate(x, t_embed, d_model)print(f'输入: {x.shape}')print(f'调制后: {x_mod.shape}')print(f'\nDiT adaLN: 条件 → MLP → (gamma, beta) → 逐层调制特征')

# 时空Patch化：视频切分为3D Patch块import numpy as np def spatiotemporal_patchify(video, patch_size=16, temporal_patch=2):    T, H, W, C = video.shape    n_t = T // temporal_patch    n_h = H // patch_size    n_w = W // patch_size    n_patches = n_t * n_h * n_w    print(f'输入视频: {T}帧 x {H}x{W} x {C}通道')    print(f'Patch网格: {n_t}(时间) x {n_h}x{n_w}(空间) = {n_patches}个Patch')    patches = []    for t in range(n_t):        for h in range(n_h):            for w in range(n_w):                patch = video[t*temporal_patch:(t+1)*temporal_patch, h*patch_size:(h+1)*patch_size, w*patch_size:(w+1)*patch_size, :]                patches.append(patch.flatten())    patches = np.array(patches)    print(f'Patch矩阵: {patches.shape}')    return patches video = np.random.rand(16, 256, 256, 3)patches = spatiotemporal_patchify(video, patch_size=32, temporal_patch=2)print(f'每个Patch维度: {patches.shape[1]}')

# 分类器自由引导(CFG)import numpy as np def classifier_free_guidance(noise_cond, noise_uncond, guidance_scale=7.5):    noise_guided = noise_uncond + guidance_scale * (noise_cond - noise_uncond)    return noise_guided guidance_scales = [1.0, 3.0, 7.5, 15.0]print('CFG效果:')for s in guidance_scales:    text_match = min(95, 50 + s * 5)    diversity = max(30, 90 - s * 6)    print(f'  s={s:.1f}: 文本匹配度≈{text_match}%, 多样性≈{diversity}%')print('\nCFG: 噪声 = 无条件噪声 + s × (有条件噪声 - 无条件噪声)')

# DiT vs U-Net 可扩展性对比import numpy as np def dit_scaling(params_M):    return 50 + 20 * np.log(params_M / 100 + 1) def unet_scaling(params_M):    return 50 + 25 * (1 - np.exp(-params_M / 800)) params_range = np.array([100, 300, 600, 1000, 2000, 5000, 10000])print('可扩展性对比 (FVD, 越低越好):')for p in params_range:    dit_fvd = 200 - dit_scaling(p)    unet_fvd = 200 - unet_scaling(p)    print(f'  {p}M: DiT={dit_fvd:.1f}, U-Net={unet_fvd:.1f}, 差异={unet_fvd-dit_fvd:+.1f}')print('\n结论: 参数量越大, DiT优势越明显')

# Sora计算资源需求估算import numpy as np def estimate_sora_compute(resolution, duration_sec, fps=30, patch_size=32, temporal_patch=2):    H, W = resolution, resolution    n_spatial = (H // patch_size) * (W // patch_size)    n_temporal = (duration_sec * fps) // temporal_patch    n_tokens = n_spatial * n_temporal    attn_flops = n_tokens ** 2    print(f'视频: {resolution}x{resolution}, {duration_sec}秒')    print(f'Token数: {n_tokens:,}')    print(f'注意力FLOPs: {attn_flops:.2e}')    return n_tokens for res, dur in [(256, 5), (512, 10), (768, 60)]:    tokens = estimate_sora_compute(res, dur)    print() print('结论: 高分辨率长视频的计算需求极高')

import numpy as np def layer_norm(x, eps=1e-5):    mean = x.mean(axis=-1, keepdims=True)    std = x.std(axis=-1, keepdims=True)    return (x - mean) / (std + eps) def adaLN_modulate(x, cond_embed, d_model):    W_mlp = np.random.randn(d_model, d_model * 2) * 0.02    params = cond_embed @ W_mlp    gamma = params[..., :d_model]    beta = params[..., d_model:]    x_norm = layer_norm(x)    return (1 + gamma) * x_norm + beta def spatiotemporal_patchify(video, patch_size=32, temporal_patch=2):    T, H, W, C = video.shape    n_t = T // temporal_patch    n_h = H // patch_size    n_w = W // patch_size    patches = []    for t in range(n_t):        for h in range(n_h):            for w in range(n_w):                patch = video[t*temporal_patch:(t+1)*temporal_patch, h*patch_size:(h+1)*patch_size, w*patch_size:(w+1)*patch_size, :]                patches.append(patch.flatten())    return np.array(patches), n_t, n_h, n_w def cross_attention(video_tokens, text_tokens, d_model):    W_q = np.random.randn(d_model, d_model) * 0.02    W_k = np.random.randn(d_model, d_model) * 0.02    W_v = np.random.randn(d_model, d_model) * 0.02    Q = video_tokens @ W_q    K = text_tokens @ W_k    V = text_tokens @ W_v    scores = Q @ K.transpose(0, 2, 1) / np.sqrt(d_model)    attn = np.exp(scores - scores.max(axis=-1, keepdims=True))    attn = attn / attn.sum(axis=-1, keepdims=True)    return attn @ V def cfg_guidance(noise_cond, noise_uncond, scale=7.5):    return noise_uncond + scale * (noise_cond - noise_uncond) d_model = 768video = np.random.rand(8, 128, 128, 3)patches, n_t, n_h, n_w = spatiotemporal_patchify(video, patch_size=32, temporal_patch=2)print(f'视频: {video.shape} → {patches.shape[0]}个时空Patch')print(f'Patch网格: {n_t}×{n_h}×{n_w}') video_tok = np.random.randn(1, patches.shape[0], d_model)text_tok = np.random.randn(1, 20, d_model)cross_out = cross_attention(video_tok, text_tok, d_model)print(f'交叉注意力输出: {cross_out.shape}') t_embed = np.random.randn(1, d_model)modulated = adaLN_modulate(video_tok, t_embed, d_model)print(f'adaLN调制后: {modulated.shape}') noise_c = np.random.randn(*video_tok.shape)noise_u = np.random.randn(*video_tok.shape)guided = cfg_guidance(noise_c, noise_u, scale=7.5)print(f'CFG引导后: {guided.shape}')print(f'\nSora: 视频→时空Patch→DiT(adaLN+交叉注意力+CFG)→去噪→视频')