{
  "paper_id": "pyramidal-flow-matching",
  "paper_title": "Pyramidal Flow Matching for Efficient Video Generative Modeling",
  "D1": [
    {
      "id": "pyramidal-flow-matching-D1-001",
      "claim": "Pyramidal flow matching uses K=3 pyramid stages for multi-scale generation",
      "source": "Section 4.1; Appendix B"
    },
    {
      "id": "pyramidal-flow-matching-D1-002",
      "claim": "pyramid stage resolution schedule: 3 (K=3) uniform time window partitions of [0,1]; each successive stage doubles spatial resolution (factor 2 per stage: 1/8, 1/4, 1/2, 1/1)",
      "source": "Section 3.2; Section 4.1"
    },
    {
      "id": "pyramidal-flow-matching-D1-003",
      "claim": "corrective noise covariance off-diagonal element (lower bound for semidefiniteness): γ = -1/3",
      "source": "Section 3.2.2, Eq 14; Appendix A, Eq 25-26"
    },
    {
      "id": "pyramidal-flow-matching-D1-004",
      "claim": "corrective noise weight at jump points: α = √3(1−s_k)/2",
      "source": "Section 3.2.2, Eq 15; Appendix A, Eq 26"
    },
    {
      "id": "pyramidal-flow-matching-D1-005",
      "claim": "endpoint timestep constraint from jump point matching (e_{k+1} > s_k, timestep rolls back): e_{k+1} = 2s_k/(1+s_k)",
      "source": "Section 3.2.2, Eq 15; Appendix A, Eq 26"
    },
    {
      "id": "pyramidal-flow-matching-D1-006",
      "claim": "upsampled endpoint rescaling factor at jump points: rescaling coefficient = (1+s_k)/2 when e_{k+1}=2s_k/(1+s_k) and γ=-1/3",
      "source": "Section 3.2.2, Eq 15; Appendix A"
    },
    {
      "id": "pyramidal-flow-matching-D1-007",
      "claim": "history condition corruptive noise range: corruptive noise strength uniformly sampled from [0, 1/3]",
      "source": "Section 3.3; Section 4.1"
    },
    {
      "id": "pyramidal-flow-matching-D1-008",
      "claim": "VAE latent compression factor: 3D VAE compression ratio: 8×8×8 (spatial × spatial × temporal)",
      "source": "Section 4.1; Appendix B"
    },
    {
      "id": "pyramidal-flow-matching-D1-009",
      "claim": "MM-DiT model size: 24 transformer layers, 2B total parameters",
      "source": "Section 4.1; Appendix B"
    },
    {
      "id": "pyramidal-flow-matching-D1-010",
      "claim": "Stage 1 training hyperparameters: lr=1e-4, batch_size=1536, steps=50k, warmup=1k, weight_decay=1e-4, grad_clip=1.0",
      "source": "Appendix B, Table 4"
    },
    {
      "id": "pyramidal-flow-matching-D1-011",
      "claim": "Stage 1 AdamW optimizer betas and epsilon: β1=0.9, β2=0.999, ε=1e-6",
      "source": "Appendix B, Table 4"
    },
    {
      "id": "pyramidal-flow-matching-D1-012",
      "claim": "Stage 1 hardware and precision: 128 NVIDIA A100 GPUs, bfloat16 precision",
      "source": "Appendix B, Table 4"
    },
    {
      "id": "pyramidal-flow-matching-D1-013",
      "claim": "Stage 2 training hyperparameters: lr=1e-4, batch_size=768, steps=200k (80k on 2s videos + 120k on 5s videos), warmup=1k, weight_decay=1e-4, grad_clip=1.0",
      "source": "Appendix B, Table 4"
    },
    {
      "id": "pyramidal-flow-matching-D1-014",
      "claim": "Stage 2 AdamW optimizer betas and epsilon: β1=0.9, β2=0.95, ε=1e-6",
      "source": "Appendix B, Table 4"
    },
    {
      "id": "pyramidal-flow-matching-D1-015",
      "claim": "Stage 2 hardware and precision: 128 NVIDIA A100 GPUs, bfloat16 precision",
      "source": "Appendix B, Table 4"
    },
    {
      "id": "pyramidal-flow-matching-D1-016",
      "claim": "Stage 2 image data mixing ratio: 12.5% image data from Stage 1 mixed into each batch",
      "source": "Appendix B"
    },
    {
      "id": "pyramidal-flow-matching-D1-017",
      "claim": "Stage 3 training hyperparameters: lr=5e-5, batch_size=384, steps=50k, warmup=1k, weight_decay=1e-4, grad_clip=1.0",
      "source": "Appendix B, Table 4"
    },
    {
      "id": "pyramidal-flow-matching-D1-018",
      "claim": "Stage 3 AdamW optimizer betas and epsilon: β1=0.9, β2=0.95, ε=1e-6",
      "source": "Appendix B, Table 4"
    },
    {
      "id": "pyramidal-flow-matching-D1-019",
      "claim": "Stage 3 hardware and precision: 128 NVIDIA A100 GPUs, bfloat16 precision",
      "source": "Appendix B, Table 4"
    },
    {
      "id": "pyramidal-flow-matching-D1-020",
      "claim": "total training compute: 20.7k A100 GPU hours total training time",
      "source": "Section 4.2; Abstract"
    },
    {
      "id": "pyramidal-flow-matching-D1-021",
      "claim": "generated video output specifications: 5s videos at 121 frames, 10s videos at 241 frames, both 768p resolution, 24 FPS",
      "source": "Section 4.1; Section 4.2; Section 4.3"
    },
    {
      "id": "pyramidal-flow-matching-D1-022",
      "claim": "token count reduction per sample: ≤15,360 tokens vs 119,040 tokens for full-sequence diffusion (10s, 241-frame video)",
      "source": "Introduction; Section 4.2"
    },
    {
      "id": "pyramidal-flow-matching-D1-023",
      "claim": "Stage 1 image data: LAION-5B count: 180M images from LAION-5B high-aesthetic subset",
      "source": "Appendix B"
    },
    {
      "id": "pyramidal-flow-matching-D1-024",
      "claim": "Stage 1 image data: CC-12M count: 11M images from CC-12M",
      "source": "Appendix B"
    },
    {
      "id": "pyramidal-flow-matching-D1-025",
      "claim": "Stage 1 image data: SA-1B count: 6.9M non-blurred images from SA-1B",
      "source": "Appendix B"
    },
    {
      "id": "pyramidal-flow-matching-D1-026",
      "claim": "Stage 1 image data: JourneyDB count: 4.4M images from JourneyDB",
      "source": "Appendix B"
    },
    {
      "id": "pyramidal-flow-matching-D1-027",
      "claim": "Stage 1 image data: synthetic data count: 14M publicly available synthetic images",
      "source": "Section 4.1"
    },
    {
      "id": "pyramidal-flow-matching-D1-028",
      "claim": "video training data counts: WebVid-10M, OpenVid-1M, plus ~1M non-watermark videos -> ~10M single-shot videos postprocessing",
      "source": "Section 4.1; Appendix B"
    },
    {
      "id": "pyramidal-flow-matching-D1-029",
      "claim": "inference speed: 56 seconds to generate a 5-second 384p video clip at inference",
      "source": "Section 4.2"
    },
    {
      "id": "pyramidal-flow-matching-D1-030",
      "claim": "VBench evaluation dimensions count: 16 fine-grained dimensions in VBench",
      "source": "Section 4.1"
    },
    {
      "id": "pyramidal-flow-matching-D1-031",
      "claim": "EvalCrafter evaluation metrics count: approximately 17 objective metrics in EvalCrafter",
      "source": "Section 4.1"
    },
    {
      "id": "pyramidal-flow-matching-D1-032",
      "claim": "user study configuration: 50 prompts sampled from VBench, 20+ participants, 3 preference dimensions (aesthetic quality, motion smoothness, semantic alignment)",
      "source": "Section 4.3; Appendix B"
    }
  ],
  "D2": [
    {
      "id": "pyramidal-flow-matching-D2-001",
      "claim": "Full spatial pyramidal flow interpolation: x_hat_t = t * x_1 XOR (1-t) * Down(x_0, 2^K), where XOR denotes interpolation between latents of different resolutions, Down(., 2^K) downsamples noise to 1/2^K resolution, K is the number of pyramid stages. This is decomposed into K piecewise time windows [s_k, e_k] each operating at successively halved resolutions.",
      "source": "Section 3.2, Eq 5-6"
    },
    {
      "id": "pyramidal-flow-matching-D2-002",
      "claim": "Piecewise flow within each pyramid stage k: For the k-th time window [s_k, e_k], let t' = (t-s_k)/(e_k-s_k) be the rescaled timestep. Within this window: x_hat_t = t' * Down(x_{e_k}, 2^k) + (1-t') * Up(Down(x_{s_k}, 2^{k+1})). Where Up is nearest/bilinear upsampling and Down is nearest/bilinear downsampling. Only stage k=0 operates at full resolution; stages k>0 use progressively lower resolutions.",
      "source": "Section 3.2, Eq 6-7"
    },
    {
      "id": "pyramidal-flow-matching-D2-003",
      "claim": "Coupled noise endpoint sampling for unified training: Sample shared noise n ~ N(0, I). Then jointly compute: Endpoint: x_hat_{e_k} = e_k * Down(x_1, 2^k) + (1-e_k) * n. Starting point: x_hat_{s_k} = s_k * Up(Down(x_1, 2^{k+1})) + (1-s_k) * n. This coupling creates organized parallel trajectories with fewer intersections, improving flow straightness compared to independent endpoint sampling.",
      "source": "Section 3.2.1, Eq 9-10; Appendix C.4, Figure 13"
    },
    {
      "id": "pyramidal-flow-matching-D2-004",
      "claim": "Unified pyramidal flow matching training objective: L = E_{k,t,(x_hat_{e_k},x_hat_{s_k})} ||v_t(x_hat_t) - (x_hat_{e_k} - x_hat_{s_k})||^2. The target vector field (x_hat_{e_k} - x_hat_{s_k}) jointly encodes both generation (noise->data) and decompression (low-res->high-res). All K pyramid stages are optimized together in a single DiT via a joint loss that sums across uniformly sampled stages.",
      "source": "Section 3.2.1, Eq 11"
    },
    {
      "id": "pyramidal-flow-matching-D2-005",
      "claim": "Corrective renoising at pyramid stage jump points (inference): At each jump point between stage k+1 and stage k: x_hat_{s_k} = ((1+s_k)/2) * Up(x_hat_{e_{k+1}}) + (sqrt(3)*(1-s_k)/2) * n', where n' ~ N(0, Sigma') with blockwise covariance Sigma'_block having diagonal=1 and off-diagonal=gamma=-1/3 (decorrelating 4x4 blocks from nearest-neighbor upsampling). The constraint e_{k+1} = 2s_k/(1+s_k) matches the distribution means. e_{k+1} > s_k means the timestep rolls back slightly at each jump.",
      "source": "Section 3.2.2, Eq 12-16; Appendix A, Eq 18-26"
    },
    {
      "id": "pyramidal-flow-matching-D2-006",
      "claim": "Temporal pyramid autoregressive conditioning (training mode): At pyramid stage k, each training latent x_hat_t^i is conditioned on compressed lower-resolution history: ... -> Down(x_{t'}^{i-2}, 2^{k+1}) -> Down(x_{t'}^{i-1}, 2^k) -> x_hat_t^i. The subscript t' indicates corruptive noise is added to history latents during training: noise strength uniformly sampled from [0, 1/3] is added to each history latent to mitigate autoregressive error accumulation.",
      "source": "Section 3.3, Eq 17"
    },
    {
      "id": "pyramidal-flow-matching-D2-007",
      "claim": "Temporal pyramid autoregressive conditioning (inference mode): During inference, clean generated frames are used as conditions: ... -> Down(x_1^{i-2}, 2^{k+1}) -> Down(x_1^{i-1}, 2^k) -> x_hat_t^i. No corruptive noise is added. The current frame's generation at the current pyramid stage uses previously generated clean frames at progressively compressed resolutions as conditions.",
      "source": "Section 3.3, Eq 18"
    },
    {
      "id": "pyramidal-flow-matching-D2-008",
      "claim": "Spatial pyramid theoretical efficiency bounds: With K pyramid stages at successively halved resolutions (factor 2 per stage) and uniform stage partitioning: (a) Initial noise is compressed by factor 2^K via Down(x_0, 2^K) — for K=3 this is 8x downsampling. (b) Computational cost reduces to approximately 1/K of full-resolution training — for K=3 this is ~1/3. Only the final stage (k=0) operates at full resolution; earlier stages use progressively lower resolutions with quadratic token savings.",
      "source": "Section 3.2, Eq 5-7"
    },
    {
      "id": "pyramidal-flow-matching-D2-009",
      "claim": "Temporal pyramid token and computation reduction formulas: For K-resolution temporal pyramid conditioning: (a) Token count reduction: 1/4^K (i.e., 1/64 for K=3). (b) Computation reduction: 1/16^K (i.e., 1/4096 for K=3). (c) Most frames computed at 1/2^K resolution (1/8 for K=3). (d) Training efficiency improvement: up to 16^K/T times (4096/T for K=3). Concrete instanced result: ≤15,360 tokens vs 119,040 tokens for full-sequence diffusion on a 10-second 241-frame video.",
      "source": "Section 3.3"
    },
    {
      "id": "pyramidal-flow-matching-D2-010",
      "claim": "Blockwise causal attention in DiT transformer layers: In each transformer layer, apply blockwise causal attention with mask M where M_{ij} = 0 if token j belongs to frame ≤ frame(i), else -∞ (preventing attention). Per-frame formulation: Attention_i^{(l)} = softmax(Q_i^{(l)} · [K_{≤f(i)}^{(l)}]^T / √d + M_i) · V_{≤f(i)}^{(l)}, where f(i) is the frame index of token i, and [K_{≤f}] concatenates keys from current and all preceding frames. Each token in a latent frame can attend to all tokens in that frame and all tokens in preceding frames, but CANNOT attend to tokens in subsequent frames. This keeps the history condition fixed and unaffected by ongoing generation, stabilizing autoregressive video generation. Full-sequence (non-factorized) attention is used across all tokens, since the pyramid representation already reduces token counts sufficiently.",
      "source": "Section 3.4; Appendix C.2, Figure 11"
    },
    {
      "id": "pyramidal-flow-matching-D2-011",
      "claim": "Position encoding scheme for multi-resolution pyramid: Two position encoding strategies: (1) Spatial dimensions: sinusoidal position encoding extrapolated to handle varying spatial resolutions across pyramid stages (better fine-grained detail at higher resolutions). (2) Temporal dimension: 1D Rotary Position Embedding (RoPE) with interpolation applied to spatially align history conditions across different temporal pyramid resolutions. Spatial extrapolation + temporal interpolation.",
      "source": "Section 3.4, Figure 3b; Section 4.1"
    },
    {
      "id": "pyramidal-flow-matching-D2-012",
      "claim": "Patch n' Pack length-balanced training batch construction: Given samples s_i with token counts n_i = H_i × W_i × T_i, pack into batch B = {s_1, ..., s_b} such that Σ_i n_i ≈ N_target (fixed token budget) and inter-sample attention masks prevent cross-sample crosstalk: M_{ij}^{inter} = -∞ if sample(i) ≠ sample(j). Packing procedure: (Step 1) Sort samples by token count, (Step 2) Greedy-bin-pack into batches reaching N_target, (Step 3) Concatenate latent sequences with sample-separated position encodings. This follows Patch n' Pack (Dehghani et al., 2023). Images keep original aspect ratios arranged into buckets. Joint training of images and videos is naturally supported since the first video frame acts as an image condition.",
      "source": "Section 3.4"
    },
    {
      "id": "pyramidal-flow-matching-D2-013",
      "claim": "Classifier-free guidance at inference: During inference sampling, classifier-free guidance is employed to enhance temporal consistency and motion smoothness of generated videos. The CFG formulation: v̂_θ(x_t, t, c) = v_θ(x_t, t, ∅) + ω · (v_θ(x_t, t, c) - v_θ(x_t, t, ∅)), where v_θ is the learned velocity field, c is the text conditioning (T5 + CLIP embeddings), ∅ is the null-condition embedding, and ω is the guidance weight. Combines conditional and unconditional velocity predictions with weight ω controlling the fidelity-diversity tradeoff.",
      "source": "Section 3.4; Section 4.1"
    },
    {
      "id": "pyramidal-flow-matching-D2-014",
      "claim": "3D VAE with causal convolution for video compression: 3D VAE compresses videos at 8x8x8 (spatial x spatial x temporal) using a MAGVIT-v2-like architecture. Key features: (a) 3D causal convolution ensures each encoded frame depends only on preceding frames. (b) Asymmetric encoder-decoder structure. (c) Kullback-Leibler (KL) regularization applied to latents. Trained from scratch on WebVid-10M and 6.9M SAM non-blurred images. Long videos are scattered across multiple GPUs for distributed tokenization.",
      "source": "Section 4.1; Appendix B"
    },
    {
      "id": "pyramidal-flow-matching-D2-015",
      "claim": "Text encoding pipeline: T5 + CLIP dual encoders: c = Concat(Embed_T5(prompt), Embed_CLIP(prompt)) ∈ ℝ^{L_T5 + L_CLIP × d_model}, where Embed_T5(·) produces L_T5 token embeddings from T5 encoder, Embed_CLIP(·) produces L_CLIP = 77 token embeddings (padded/truncated) from CLIP text encoder, following FLUX.1 (Black Forest Labs, 2024). The MM-DiT uses cross-attention to condition on the concatenated c: CrossAttn(x, c) = softmax(Q_x · K_c^T / √d) · V_c, where Q_x = x W_Q, K_c = c W_K, V_c = c W_V.",
      "source": "Section 4.1; Appendix B"
    },
    {
      "id": "pyramidal-flow-matching-D2-016",
      "claim": "Three-stage training procedure: Three-stage progressive training with increasing resolution and temporal length: Stage 1 (Image-only pre-training) on pure image datasets — establishes visual pixel dependencies. Stage 2 (Low-resolution video training) on WebVid-10M + OpenVid-1M + ~1M non-watermark videos recaptioned with Video-LLaMA2, trained progressively on 2s then 5s videos, with 12.5% image data from Stage 1 mixed per batch. Stage 3 (High-resolution video fine-tuning) on 5-10s high-resolution videos. All stages use AdamW optimizer with constant learning rate and 1k-step warmup. See D1 for exact hyperparameter values.",
      "source": "Appendix B, Table 4"
    },
    {
      "id": "pyramidal-flow-matching-D2-017",
      "claim": "Image-to-video generation via autoregressive frame prediction: Given a static input image (first frame) and a text prompt, autoregressively predict future frames using the trained model without fine-tuning. The causal attention design ensures each new frame is conditioned on all previous frames. The model outputs 120 new frames spanning 5 seconds at 768p 24fps (for image-to-video), ending with the final frame of the video clip.",
      "source": "Section 4.3, Figure 6"
    }
  ],
  "D3": [
    {
      "id": "pyramidal-flow-matching-D3-001",
      "claim": "Text-to-Video Generation Evaluation on VBench: Generate 5-second, 121-frame, 768p, 24fps videos from VBench text prompts. Compare against public-data models (Open-Sora Plan v1.3, Open-Sora 1.2, VideoCrafter2, T2V-Turbo) and proprietary models (CogVideoX-2B/5B, Pika 1.0, Gen-2, Kling, Gen-3 Alpha). Evaluate across all 16 VBench dimensions grouped into Total Score, Quality Score, and Semantic Score.",
      "source": "Section 4.1; Section 4.3, Table 1, Table 5"
    },
    {
      "id": "pyramidal-flow-matching-D3-002",
      "claim": "Text-to-Video Generation Evaluation on EvalCrafter: Generate 5-second, 768p, 24fps videos from EvalCrafter text prompts. Compare against public-data models (ModelScope, Show-1, VideoCrafter2) and proprietary models (LaVie, Pika 1.0, Gen-2). Evaluate across approximately 17 objective metrics covering visual quality, motion quality, and semantic alignment.",
      "source": "Section 4.1; Section 4.3, Table 2, Table 6"
    },
    {
      "id": "pyramidal-flow-matching-D3-003",
      "claim": "User Study on Human Preference: Sample 50 prompts from VBench, randomly sample one generated video per prompt from each of 6 baseline models (Open-Sora Plan V1.1, Open-Sora 1.2, Pika 1.0, CogVideoX-2B, CogVideoX-5B, Kling). Pair each baseline's video with the Pyramidal Flow Matching model's video. 20+ participants rank preference across three dimensions: aesthetic quality, motion smoothness, semantic alignment. Watermarks and model identifiers removed. Total of 1411 valid preference choices collected.",
      "source": "Section 4.3, Figure 4; Appendix B, Figure 9"
    },
    {
      "id": "pyramidal-flow-matching-D3-004",
      "claim": "Spatial Pyramid Ablation Study (Image Generation): Compare pyramidal flow matching against standard flow matching on text-to-image generation. Both variants use same training data, tokens per batch, hyperparameters, and model architecture. Train for 50k image steps. Evaluate FID on MS-COCO validation set with 3K randomly sampled prompts. Also compare qualitative visual quality and prompt-following capability.",
      "source": "Section 4.4, Figure 7"
    },
    {
      "id": "pyramidal-flow-matching-D3-005",
      "claim": "Temporal Pyramid Ablation Study (Video Generation): Compare pyramidal flow matching against full-sequence diffusion on video generation. Both variants use same experimental settings. Train for 100k low-resolution video steps. Compare visual quality, temporal consistency, motion coherence, and artifact levels qualitatively via keyframe visualization.",
      "source": "Section 4.4, Figure 8"
    },
    {
      "id": "pyramidal-flow-matching-D3-006",
      "claim": "Corrective Renoising Ablation Study: Train a spatial pyramid variant that omits the corrective Gaussian noise at jump points during inference (no renoising, only upsampling at resolution transitions). Compare against full pyramidal flow with corrective renoising (gamma=-1/3, alpha=sqrt(3)*(1-s_k)/2). Evaluate image quality qualitatively — examine block-like artifacts, fine-grained detail, color vividness.",
      "source": "Appendix C.2, Figure 10"
    },
    {
      "id": "pyramidal-flow-matching-D3-007",
      "claim": "Causal Attention Ablation Study: Train a model variant using bidirectional (non-causal) attention across all latent frames instead of blockwise causal attention. Compare against the default causal attention model. Train both for 100k steps. Evaluate 1-second video generation quality: visual quality, temporal coherence (subject shape/color constancy), motion quality.",
      "source": "Appendix C.2, Figure 11"
    },
    {
      "id": "pyramidal-flow-matching-D3-008",
      "claim": "Image-to-Video Generation Evaluation: Given static input images and text prompts, autoregressively generate future frames (120 frames, 5-second duration, 768p, 24fps) using the trained text-to-video model without any fine-tuning. Qualitative evaluation of motion prediction quality and temporal dynamics. Compare with no baselines (demonstration of emergent capability).",
      "source": "Section 4.3, Figure 6"
    },
    {
      "id": "pyramidal-flow-matching-D3-009",
      "claim": "Three-Stage Training Pipeline with Specific Data Configuration: (1) Image-only training on ~180M LAION-5B, 11M CC-12M, 6.9M SA-1B, 4.4M JourneyDB, 14M synthetic images for 50k steps at lr=1e-4, batch=1536, 128 A100 GPUs. (2) Low-resolution video training on WebVid-10M + OpenVid-1M + ~1M non-watermark (captioned via Video-LLaMA2) for 200k steps at lr=1e-4, batch=768, 128 A100 GPUs, with 12.5% image data mixing. (3) High-resolution video fine-tuning on 5-10s videos for 50k steps at lr=5e-5, batch=384, 128 A100 GPUs. All using AdamW, bfloat16, constant lr with 1k warmup, weight_decay=1e-4, grad_clip=1.0. Total: 20.7k A100 GPU hours.",
      "source": "Section 4.1; Appendix B, Table 4"
    }
  ],
  "D4": [
    {
      "id": "pyramidal-flow-matching-D4-001",
      "claim": "Spatial Pyramid Flow Method Execution Pipeline: 1. Flow matching ODE with linear interpolation path (dx_t/dt = v_t(x_t), x_t = t*x_1 + (1-t)*x_0); 2. Full spatial pyramidal flow interpolation (decompose full [0,1] trajectory into K piecewise time windows at halved resolutions); 3. Piecewise flow within each pyramid stage k (rescaled timestep t', Down/Up operations between resolutions); 4. Coupled noise endpoint sampling for unified training (shared noise n couples all stage endpoints, producing parallel trajectories); 5. Unified pyramidal flow matching training objective (single loss jointly encodes generation + decompression across all K stages); 6. Corrective renoising at pyramid stage jump points during inference (blockwise-correlated noise at resolution transitions prevents block artifacts)",
      "source": "Section 3.1-3.2.2"
    },
    {
      "id": "pyramidal-flow-matching-D4-002",
      "claim": "Temporal Pyramid Autoregressive Conditioning Pipeline (Generation Phase 2, built on Spatial Pyramid pipeline): Entry — the spatial pyramid flow matching pipeline handles per-frame generation and decompression across K=3 resolution levels; the MM-DiT receives text embeddings from T5+CLIP dual encoders. For each autoregressively generated frame i at pyramid stage k, this phase constructs compressed temporal history conditions from prior frames: frame i-2 and earlier downsampled to resolution 2^(k+1), frame i-1 downsampled to 2^k. Training (Section 3.3, Eq.17): corruptive noise uniformly sampled from [0, 1/3] is added to each history latent to mitigate autoregressive error accumulation. Inference (Eq.18): clean generated frames serve as compressed history, no noise added. Exit — the temporal conditions feed into the MM-DiT's blockwise causal attention layers (Section 3.4) alongside the current noisy latent and text embeddings, driving the autoregressive video generation loop. Active across all three training stages (the three-stage training pipeline) and inference; reduces token count by up to 1/4^K and computation by up to 1/16^K vs full-sequence diffusion.",
      "source": "Section 3.3, Eq 17-18"
    },
    {
      "id": "pyramidal-flow-matching-D4-003",
      "claim": "Three-Stage Training Pipeline: Stage 1: Image-only pre-training — 50k steps, lr=1e-4, batch=1536, AdamW(0.9,0.999), 128 A100 GPUs, ~12h; Stage 2: Low-resolution video training — 80k steps on 2s videos, then 120k steps on 5s videos, lr=1e-4, batch=768, AdamW(0.9,0.95), 128 A100 GPUs, 12.5% image mixing, ~90h; Stage 3: High-resolution video fine-tuning — 50k steps on 5-10s videos, lr=5e-5, batch=384, AdamW(0.9,0.95), 128 A100 GPUs, ~60h",
      "source": "Section 4.1; Appendix B, Table 4"
    },
    {
      "id": "pyramidal-flow-matching-D4-004",
      "claim": "VBench Text-to-Video Evaluation Protocol: Complete three-stage training pipeline; Generate 5-second, 121-frame, 768p, 24fps videos from VBench text prompts; Evaluate across all 16 VBench dimensions against 10 baselines (4 public-data + 6 proprietary)",
      "source": "Section 4.1; Section 4.3, Table 1, Table 5"
    },
    {
      "id": "pyramidal-flow-matching-D4-005",
      "claim": "EvalCrafter Text-to-Video Evaluation Protocol: Complete three-stage training pipeline; Generate 5-second, 768p, 24fps videos from EvalCrafter text prompts; Evaluate across ~17 objective metrics against 6 baselines",
      "source": "Section 4.1; Section 4.3, Table 2, Table 6"
    },
    {
      "id": "pyramidal-flow-matching-D4-006",
      "claim": "User Study Protocol (Evaluation Phase 3, after VBench and EvalCrafter automated benchmarks): Entry — the three-stage training pipeline has completed, producing a fully trained 2B-parameter MM-DiT model that generates 5s, 768p, 24fps videos; automated VBench and EvalCrafter evaluations have been executed. Protocol: Sample 50 prompts from VBench; generate one video from the Pyramidal Flow Matching model and one from each of 6 baseline models (Open-Sora Plan V1.1, Open-Sora 1.2, Pika 1.0, CogVideoX-2B, CogVideoX-5B, Kling); pair the Pyramidal Flow Matching model's video with each baseline's, removing watermarks and model identifiers for blind pairwise comparison; 20+ human participants rank preference across 3 dimensions (aesthetic quality, motion smoothness, semantic alignment). Exit — 1411 valid preference choices collected, providing human-preference validation that complements automated metrics. Result: Pyramidal Flow Matching model preferred on motion smoothness due to 24fps output vs baselines' typical 8fps limitation.",
      "source": "Section 4.3, Figure 4; Appendix B, Figure 9"
    },
    {
      "id": "pyramidal-flow-matching-D4-007",
      "claim": "Spatial Pyramid Ablation Protocol: Train pyramidal flow matching variant and standard flow matching baseline for 50k image steps (same data, tokens, hyperparameters, architecture); Evaluate FID on MS-COCO validation set (3K randomly sampled prompts) at regular intervals; Compare convergence curves, visual quality, and prompt-following capability",
      "source": "Section 4.4, Figure 7"
    },
    {
      "id": "pyramidal-flow-matching-D4-008",
      "claim": "Temporal Pyramid Ablation Protocol: Train pyramidal flow variant and full-sequence diffusion baseline for 100k low-resolution video steps (same settings); Qualitatively compare generated video keyframes for visual quality, temporal consistency, motion coherence, and artifacts",
      "source": "Section 4.4, Figure 8"
    },
    {
      "id": "pyramidal-flow-matching-D4-009",
      "claim": "Corrective Renoising Ablation Protocol: Train both variants with same spatial pyramid configuration; Run inference: one with corrective renoising (gamma=-1/3, alpha=sqrt(3)*(1-s_k)/2), one with upsampling only; Compare generated image quality — block artifacts, detail richness, color vividness, global structure",
      "source": "Appendix C.2, Figure 10"
    },
    {
      "id": "pyramidal-flow-matching-D4-010",
      "claim": "Causal Attention Ablation Protocol: Train bidirectional attention variant and blockwise causal attention variant each for 100k steps; Generate 1-second videos from both variants; Compare keyframe consistency and temporal coherence (subject shape/color constancy)",
      "source": "Appendix C.2, Figure 11"
    },
    {
      "id": "pyramidal-flow-matching-D4-011",
      "claim": "Image-to-Video Generation Protocol (Emergent): Train model on text-to-video only through all 3 stages (no image-to-video fine-tuning); At inference, provide a static image as the first frame together with a text prompt; Autoregressively generate 120 future frames (5 seconds, 768p, 24fps) via causal attention conditioning",
      "source": "Section 4.3, Figure 6"
    }
  ]
}