papers/ca2-vdm/sau.json

{
  "paper_id": "ca2-vdm",
  "paper_title": "CA2-VDM: Continuous Adjoint Augmented Variational Diffusion Models",
  "D1": [
    {
      "id": "ca2-vdm-D1-001",
      "claim": "CA2-VDM DDPM noise schedule: T=1000 timesteps, linear beta schedule with β₁=1e-4, β_T=0.02",
      "source": "Appendix C / DDPM noise schedule"
    },
    {
      "id": "ca2-vdm-D1-002",
      "claim": "inference denoising steps: inference_steps=100, improved DDPM",
      "source": "Appendix C / inference denoising steps"
    },
    {
      "id": "ca2-vdm-D1-003",
      "claim": "latent space configuration: resolution=256×256, VAE downsample=8x, C=4",
      "source": "Section 4.1, Table 6 / VAE from StableDiffusion (SD VAE: 8x downsample, C=4)"
    },
    {
      "id": "ca2-vdm-D1-004",
      "claim": "T2V chunk and condition lengths: l=16, P_max=49, L_train_max=65",
      "source": "Section 4.1, Appendix C / T2V chunk and condition lengths"
    },
    {
      "id": "ca2-vdm-D1-005",
      "claim": "prefix-enhanced spatial attention sub-prefix length: P'=3",
      "source": "Section 3.2 Eq.(4) / prefix-enhanced spatial attention sub-prefix length"
    },
    {
      "id": "ca2-vdm-D1-006",
      "claim": "T2V stage 1 training config: batch_size=288, steps=32k (stage 1, 32-frame, causal-only)",
      "source": "Appendix C / T2V stage 1 training config"
    },
    {
      "id": "ca2-vdm-D1-007",
      "claim": "T2V stage 2 training config: batch_size=144, steps=21k (stage 2, 65-frame, with clean prefix)",
      "source": "Appendix C / T2V stage 2 training config"
    },
    {
      "id": "ca2-vdm-D1-008",
      "claim": "learning rate and optimizer: lr=2e-5, AdamW optimizer",
      "source": "Appendix C / learning rate and optimizer"
    },
    {
      "id": "ca2-vdm-D1-009",
      "claim": "CFG scale for T2V: classifier-free guidance scale=7.5",
      "source": "Appendix C / CFG scale for T2V"
    },
    {
      "id": "ca2-vdm-D1-010",
      "claim": "Hardware for all CA2-VDM experiments: single NVIDIA A100 GPU (80GB)",
      "source": "Section 4.3 / hardware"
    },
    {
      "id": "ca2-vdm-D1-011",
      "claim": "video prediction chunk and condition lengths: l=8, P_max=25, L_train_max=33",
      "source": "Section 4.1, Appendix C / video prediction chunk and condition lengths"
    },
    {
      "id": "ca2-vdm-D1-012",
      "claim": "video prediction training config: batch_size=8, steps=11k (video prediction)",
      "source": "Appendix C / video prediction training config"
    },
    {
      "id": "ca2-vdm-D1-013",
      "claim": "baseline OS-Fix condition length: P=16 fixed (OS-Fix T2V), P=8 fixed (OS-Fix VP)",
      "source": "Section 4.1, Appendix C / baseline OS-Fix condition length"
    },
    {
      "id": "ca2-vdm-D1-014",
      "claim": "baseline OS-Fix training config: OS-Fix batch=288, 20k steps (T2V); batch=8, 11k steps (VP)",
      "source": "Appendix C / baseline OS-Fix training config"
    },
    {
      "id": "ca2-vdm-D1-015",
      "claim": "T2V training dataset: InternVid 4.9M filtered video-text pairs",
      "source": "Section 4.1, Appendix C / T2V training dataset"
    },
    {
      "id": "ca2-vdm-D1-016",
      "claim": "MSR-VTT evaluation dataset: MSR-VTT test: 2990 videos, 20 captions each",
      "source": "Appendix D.1 / MSR-VTT evaluation dataset"
    },
    {
      "id": "ca2-vdm-D1-017",
      "claim": "UCF101 evaluation dataset: UCF101: 2048 samples, uniform category distribution",
      "source": "Appendix D.1 / UCF101 evaluation dataset"
    },
    {
      "id": "ca2-vdm-D1-018",
      "claim": "SkyTimelapse dataset statistics: SkyTimelapse: 2392 train clips / 225 test clips",
      "source": "Appendix D.1 / SkyTimelapse dataset statistics"
    },
    {
      "id": "ca2-vdm-D1-019",
      "claim": "model initialization and encoders: T5 text encoder, Open-Sora v1.0 initialization, VAE from StableDiffusion",
      "source": "Section 4.1 / model initialization and encoders"
    },
    {
      "id": "ca2-vdm-D1-020",
      "claim": "KV-cache and model forward tensor shapes: KV-cache shape (1, 25, hw, C), model forward shape (1, 4, 8, 32, 32)",
      "source": "Table 6 / KV-cache and model forward tensor shapes"
    },
    {
      "id": "ca2-vdm-D1-021",
      "claim": "evaluation protocol config: AR steps: 6-7, total frames 80, FVD chunk_size=16, FVD sample_count=512",
      "source": "Section 4.2, Section 4.3, Appendix D.2 / evaluation protocol config"
    },
    {
      "id": "ca2-vdm-D1-022",
      "claim": "baseline autoregressive VDMs config: GenLV overlap=8, StreamT2V chunk=16",
      "source": "Section 4.2 / baseline autoregressive VDMs config"
    }
  ],
  "D2": [
    {
      "id": "ca2-vdm-D2-001",
      "claim": "Partial Noising Training with Distinct Timestep Embeddings: L̃_simple(θ) = E_{z,ε,t} [‖(ε_θ([z_0^{0:P}, z_t^{P:L}], t) − ε) ⊙ m‖²₂]\n\nwhere:\n- z_0^{0:P}: P consecutive clean prefix frames (uncorrupted)\n- z_t^{P:L}: remaining L−P frames as denoising target (noised to timestep t)\n- t: timestep vector with t_i = t if i ≥ P else 0 (tEmb(0) for clean prefix, tEmb(t) for denoising target)\n- m ∈ {0,1}^N: loss mask to exclude the clean prefix part (m_i = 1 if i ≥ P else 0)\n\nReference: Eq. (2) in Section 3.2; clean prefix always assigned tEmb(0), enabling cache sharing across denoising timesteps.",
      "source": "Section 3.2 Eq.(2) / Partial Noising Training with Distinct Timestep Embeddings"
    },
    {
      "id": "ca2-vdm-D2-002",
      "claim": "Combined Training Objective with Learnable Covariance (L̃_simple + L̃_vlb): L_total(θ) = L̃_simple(θ) + L̃_vlb(θ)\n\nwhere:\n- L̃_vlb(θ) = −log p_θ(z_0|z_1) + Σ_t D_KL(q(z_{t-1}|z_t,z_0) ‖ p_θ(z_{t-1}|z_t))\n- Both L̃_simple and L̃_vlb use the same timestep vector t and loss mask m\n- Σ_θ is learnable covariance (not fixed variance schedule)\n- D_KL term determined by mean μ_θ and covariance Σ_θ\n- Training optimizes combined loss L̃_simple + L̃_vlb following (Nichol & Dhariwal, 2021; Peebles & Xie, 2023)\n\nReference: Appendix B; learnable covariance improves sampling quality.",
      "source": "Section 3.2, Appendix B / Combined Training Objective with Learnable Covariance"
    },
    {
      "id": "ca2-vdm-D2-003",
      "claim": "Causal Temporal Attention: CausalAttn(Q, K, V) = Softmax(QK^T / √C' + M) V\n\nwhere:\n- Input first permuted: spatial H×W treated as batch dimension\n- Q, K, V ∈ R^{L×C'}: linearly projected from permuted input (per spatial grid)\n- M ∈ R^{L×L}: lower triangular attention mask with M_{i,j} = −∞ if i < j else 0\n- Each frame attends only to its preceding frames (unidirectional dependency)\n\nReference: Eq. (3) in Section 3.2.",
      "source": "Section 3.2 Eq.(3) / Causal Temporal Attention"
    },
    {
      "id": "ca2-vdm-D2-004",
      "claim": "Prefix-Enhanced Spatial Attention: For hidden input h_t^{0:L} ∈ R^{L×H×W×C} (L as batch dim, H×W flattened):\n\nQuery: Q̄(i) = W̄^Q h_t^i\n\nKey (prefix-enhanced):\nK̄(i) = { W^K[h_0^{P−P'}; ...; h_0^{P−1}; h_t^i]   if i ≥ P\n       { W^K[h_0^i; ...; h_0^i]                 if i < P (self-repeat P' times)\n\nSame operation for value V̄(i).\n\nAttention(Q̄, K̄, V̄) with attention map of shape (HW) × ((P'+1)HW). In practice, P' is small (e.g., P'=3) as computational cost scales proportionally with P'.\n\nReference: Eq. (4) in Section 3.2.",
      "source": "Section 3.2 Eq.(4) / Prefix-Enhanced Spatial Attention"
    },
    {
      "id": "ca2-vdm-D2-005",
      "claim": "Temporal KV-Cache with Cache Sharing Across Denoising Timesteps: At AR step k with P_k generated frames:\n\nDenoising stage:\n- Noisy Q_t^{P_k:P_k+l}, K_t^{P_k:P_k+l}, V_t^{P_k:P_k+l} ∈ R^{l×C'} (per spatial grid)\n- Read clean caches: K_0^{0:P_k}, V_0^{0:P_k} ∈ R^{P_k×C'}\n- Concatenate: K̃(k,t) = [K_0^{0:P_k}, K_t^{P_k:P_k+l}]\n              Ṽ(k,t) = [V_0^{0:P_k}, V_t^{P_k:P_k+l}]\n- Compute: CausalAttn(Q_t^{P_k:P_k+l}, K̃(k,t), Ṽ(k,t))\n  with attention map shape l × (P_k + l)\n\nClean KV-cache K_0^{0:P_k}, V_0^{0:P_k} is shared across all denoising timesteps t (cache sharing).\n\nReference: Eq. (5) in Section 3.3, Figure 4(b).",
      "source": "Section 3.3 Eq.(5) / Temporal KV-Cache with Cache Sharing"
    },
    {
      "id": "ca2-vdm-D2-006",
      "claim": "Cache Writing Stage: After denoising completes at AR step k:\n\n1. Denoised latent z_0^{P_k:P_k+l} is input to model again\n2. Compute clean temporal keys and values: K_0^{P_k:P_k+l}, V_0^{P_k:P_k+l}\n3. Update KV-cache queue:\n   K_0^{0:P_{k+1}} = concat(K_0^{0:P_k}, K_0^{P_k:P_k+l})\n   V_0^{0:P_{k+1}} = concat(V_0^{0:P_k}, V_0^{P_k:P_k+l})\n4. Updated cache used in AR step k+1 (P_{k+1} = P_k + l)\n5. When P_k reaches P_max, earliest chunk dequeued from queue\n\nReference: Section 3.3, Figure 4(c).",
      "source": "Section 3.3 / Cache Writing Stage"
    },
    {
      "id": "ca2-vdm-D2-007",
      "claim": "Cyclic Temporal Positional Embeddings (Cyclic-TPEs): Training:\n- L_train = P_max + l: maximum TPE sequence length during training\n- Each sample assigned TPE sequence cyclically shifted with random offset\n- P ∈ {1, 1+l, ..., 1+nl}, so the model learns all possible starting positions\n\nInference (KV-cache enabled, Figure 4c-right):\n- TPEs bound to keys and values at previous AR steps and stored in preceding KV-cache chunks, preventing reassignment from scratch\n- Denoising target assigned TPEs indexed from the beginning (cyclically shifted)\n- Cyclic shift offset matches the training pattern for training/inference alignment\n\nReference: Section 3.3, Figure 4(c).",
      "source": "Section 3.3 / Cyclic Temporal Positional Embeddings"
    },
    {
      "id": "ca2-vdm-D2-008",
      "claim": "Spatial KV-Cache for Prefix-Enhanced Attention: At AR step k:\n\nDenoising stage:\n- Keys/values from denoising target enhanced by spatial KV-cache (P' frames sub-prefix)\n- Spatial concatenation per Eq (4)\n\nCache writing stage:\n- Denoised latent frames first enhanced via self-repeat\n- Compute clean spatial keys and values\n- Store for one chunk only and overwrite at every AR step\n- Since P' < l, prefix enhancement only depends on the most recent generated chunk (P_k−l:P_k)\n\nReference: Section 3.3.",
      "source": "Section 3.3 / Spatial KV-Cache for Prefix-Enhanced Attention"
    },
    {
      "id": "ca2-vdm-D2-009",
      "claim": "Autoregressive Inference Loop with DDPM/DDIM Sampling: Start from given first frame(s). For each AR step k (k = 0, 1, 2, ...):\n\n1. Denoising Stage:\n   - Clean prefix: z_0^{0:P_k} (P_k previously generated frames)\n   - Denoising target: z_t^{P_k:P_k+l} (l-frame chunk, randomly initialized noise)\n   - For t = T, T−1, ..., 1:\n       Sample z_{t-1}^{P_k:P_k+l} ~ p_θ(z_{t-1}^{P_k:P_k+l} | z_t^{P_k:P_k+l}, z_0^{0:P_k})\n   - Clean prefix KV-cache shared across all timesteps (cache sharing)\n\n2. Cache Writing Stage:\n   - Input denoised z_0^{P_k:P_k+l} to model\n   - Compute clean spatial and temporal KV-caches\n   - Update KV-cache queue for next AR step (k+1)\n\nReference: Section 3.3, Figure 3(b).",
      "source": "Section 3.3 / Autoregressive Inference Loop"
    },
    {
      "id": "ca2-vdm-D2-010",
      "claim": "P_max Queue Management for Long-Term Context: Training configuration:\n- P randomly sampled from {1, 1+l, 1+2l, ..., 1+nl}\n- P_max = 1 + nl (maximum conditional frames)\n- L_train = P + l (total frames in training clip)\n- max(L_train) = P_max + l\n\nInference queue behavior:\n- At each AR step k: P_k = P_{k-1} + l (grows by chunk length)\n- When P_k reaches P_max, earliest KV-cache is dequeued to maintain fixed-length condition window\n- Cyclic-TPEs enable proper positional encoding after dequeue (cyclic shift mechanism)\n- Early KVs can be safely dequeued as new frames are primarily influenced by recent KVs\n\nReference: Section 3.3, Section 4.1.",
      "source": "Section 3.3, Section 4.1 / P_max Queue Management"
    }
  ],
  "D3": [
    {
      "id": "ca2-vdm-D3-001",
      "claim": "Zero-shot Text-to-Video FVD Evaluation (Table 1): Evaluate Ca2-VDM's in-chunk T2V generation quality against SOTA models on MSR-VTT and UCF101 test sets at resolution 16×256×256. MSR-VTT uses 2990 videos with 1 randomly selected caption per video from 20 available captions. UCF101 uses 2048 samples with uniform category distribution and PYoCo descriptive prompts. FVD computed via pretrained I3D feature extractor. Compared to two groups: text-conditioned (ModelScope, VideoComposer, Video-LDM, PYoCo, Make-A-Video) and text+image-conditioned (AnimateAnything, PixelDance, SEINE).",
      "source": "Section 4.2, Table 1, Appendix D / Zero-shot T2V FVD Evaluation"
    },
    {
      "id": "ca2-vdm-D3-002",
      "claim": "Finetuned UCF101 FVD Evaluation (Table 2): Finetune Ca2-VDM on UCF101 training set and evaluate FVD on UCF101 test set at resolution 16×256×256. Compare against SOTA video generation models (MCVD, VDT, DIGAN, TATS, VideoFusion, LVDM, PVDM, Latte). Methods marked with * trained on both train+test sets.",
      "source": "Section 4.2, Table 2 / Finetuned UCF101 FVD Evaluation"
    },
    {
      "id": "ca2-vdm-D3-003",
      "claim": "Autoregressive Temporal Consistency FVD Evaluation (Table 3): Evaluate multi-chunk temporal consistency by generating 48-frame videos with 6 AR steps (l=8 each) on MSR-VTT test set. Compute chunk-wise FVD between AR step 1 and steps 2-6. Compare Ca2-VDM against autoregressive VDMs: GenLV (overlap=8, 16-frame clips, based on AnimateDiff + DDIM inversion for first frame), StreamT2V (chunk=16, condition=8, based on SVD), OS-Fix (fixed P=16).",
      "source": "Section 4.2, Table 3 / Autoregressive Temporal Consistency FVD Evaluation"
    },
    {
      "id": "ca2-vdm-D3-004",
      "claim": "Ablation Study: P_max and Prefix-Enhancement (PE) Effectiveness (Table 4): Train Ca2-VDM variants with different P_max (25 vs 41) and with/without prefix-enhanced spatial attention on SkyTimelapse dataset for video prediction (no text). Each variant generates 49-frame videos in 6 AR steps (given first frame). Evaluate FVD of three 16-frame chunks w.r.t. 16-frame ground-truth videos.",
      "source": "Section 4.2, Table 4 / Ablation Study P_max and PE"
    },
    {
      "id": "ca2-vdm-D3-005",
      "claim": "Autoregressive Time Cost Measurement (Table 5, Figure 6): Measure accumulated wall-clock time for generating 80 frames at 256×256 on a single NVIDIA A100 GPU. Use improved DDPM with 100 denoising steps. Compare OS-Fix (P=8), OS-Ext (P_max=25), Ca2-VDM (P_max=25), and StreamT2V (results from GitHub, same device/resolution). Figure 6 shows cumulative time per AR step for P_max=25 and P_max=41 variants.",
      "source": "Section 4.3, Table 5, Figure 6 / Autoregressive Time Cost Measurement"
    },
    {
      "id": "ca2-vdm-D3-006",
      "claim": "FLOPs Computational Cost Analysis (Figure 8): Count floating-point operations for generating 56 frames (7 AR steps) with a single denoising step. Analyze FLOPs in temporal attention, spatial attention, and visual-text cross-attention layers separately. Compare Ca2-VDM vs OS-Ext across varying P_max values to demonstrate Ca2-VDM's computational efficiency from cache sharing.",
      "source": "Section 4.3, Figure 8 / FLOPs Computational Cost Analysis"
    },
    {
      "id": "ca2-vdm-D3-007",
      "claim": "GPU Memory Cost Comparison with Live2diff (Table 6): Compare GPU memory usage at T=50 denoising steps. Ca2-VDM benefits from cache sharing (KV-cache independent of T, fixed shape (1,25,hw,C)), while Live2diff stores per-timestep KV-cache (shape (T,16,h'w',C')). Report batch shape, KV-cache shape, KV-cache memory, and total GPU memory. Ca2-VDM evaluated with and without prefix-enhancement (PE).",
      "source": "Section 4.3, Table 6 / GPU Memory Cost Comparison"
    },
    {
      "id": "ca2-vdm-D3-008",
      "claim": "VBench Evaluation for Appearance and Temporal Quality (Table 7): Evaluate Ca2-VDM and OS-Ext on SkyTimelapse test set using VBench benchmark at 256×256 with P_max=25 and 6 AR steps. Assess four metrics: aesthetic quality and imaging quality (spatial/appearance), motion smoothness and temporal flickering (temporal consistency).",
      "source": "Appendix E, Table 7 / VBench Evaluation"
    }
  ],
  "D4": [
    {
      "id": "ca2-vdm-D4-001",
      "claim": "Experiment workflow for Zero-shot Text-to-Video FVD Evaluation (Table 1): Train Ca2-VDM on InternVid 4.9M filtered subset (stage 1: 32k steps, 32-frame causal-only; stage 2: 21k steps, 65-frame with clean prefix) → Generate 16-frame videos for each test sample using improved DDPM 100 steps, CFG=7.5 → Extract I3D features from generated and real videos → Compute FVD scores",
      "source": "Section 4.1, Section 4.2, Table 1, Appendix D"
    },
    {
      "id": "ca2-vdm-D4-002",
      "claim": "Experiment workflow for Finetuned UCF101 FVD Evaluation (Table 2): Finetune Ca2-VDM on UCF101 train set → Generate 16×256×256 videos on UCF101 test set → Compute FVD against real test videos",
      "source": "Section 4.2, Table 2"
    },
    {
      "id": "ca2-vdm-D4-003",
      "claim": "Experiment workflow for Autoregressive Temporal Consistency FVD Evaluation (Table 3): For each model, generate 48 frames via 6 AR steps (l=8) → Split into 3 chunks of 16 frames → Compute FVD of chunks 2,3 vs chunk 1 using I3D features → Report FVD at each AR step boundary",
      "source": "Section 4.2, Table 3, Appendix D.2"
    },
    {
      "id": "ca2-vdm-D4-004",
      "claim": "Experiment workflow for Ablation Study: Train 4 Ca2-VDM variants on SkyTimelapse train set (batch=8, 11k steps, video prediction) → Generate 49-frame videos (6 AR steps, given first frame) → Compute chunk-wise FVD for chunks 1, 2, 3 → Compare across variants",
      "source": "Section 4.2, Table 4"
    },
    {
      "id": "ca2-vdm-D4-005",
      "claim": "Experiment workflow for Autoregressive Time Cost Measurement (Table 5, Figure 6): Setup: single NVIDIA A100 GPU, improved DDPM 100 steps → Generate 80 frames with each method at 256×256 → Measure and accumulate wall-clock time at each AR step → Plot cumulative time curves for P_max=25 and P_max=41 variants",
      "source": "Section 4.3, Table 5, Figure 6"
    },
    {
      "id": "ca2-vdm-D4-006",
      "claim": "Experiment workflow for FLOPs Computational Cost Analysis (Figure 8): Fix generation config: 56 frames, 7 AR steps, 1 denoising step → For each P_max value, run model forward and count FLOPs per attention layer → Plot stacked FLOPs by layer type vs P_max → Compare Ca2-VDM (only temporal grows) vs OS-Ext (all layers grow)",
      "source": "Section 4.3, Figure 8"
    },
    {
      "id": "ca2-vdm-D4-007",
      "claim": "Experiment workflow for GPU Memory Cost Comparison with Live2diff (Table 6): Run Ca2-VDM w/ PE and w/o PE at T=50, measure GPU memory → Ca2-VDM: model forward (1,4,8,32,32), KV-cache (1,25,hw,C) → Compare KV-cache memory: Ca2-VDM 0.77-0.86GB vs Live2diff 17.70GB → Compare total memory: Ca2-VDM 3.95-4.79GB vs Live2diff 29.46GB",
      "source": "Section 4.3, Table 6"
    },
    {
      "id": "ca2-vdm-D4-008",
      "claim": "Experiment workflow for VBench Evaluation for Appearance and Temporal Quality (Table 7): Generate videos with Ca2-VDM and OS-Ext: P_max=25, 6 AR steps, 256×256 → Evaluate all four VBench metrics → Compare spatial quality and temporal consistency between methods",
      "source": "Appendix E, Table 7"
    }
  ]
}