Dynamic View Synthesis as an Inverse Problem
Authors: Hidir Yesiltepe
Pinar Yanardag
Venue: NeurIPS 2025 poster ()
Keywords: diffusion; camera; motion; video
Primary area: applications
TL;DR: We propose a novel dynamic view synthesis method by approaching Dynamic View Synthesis as an Inverse Problem.

Abstract: In this work, we address dynamic view synthesis from monocular videos as an inverse problem in a training-free setting. By redesigning the noise initialization phase of a pre-trained video diffusion model, we enable high-fidelity dynamic view synthesis without any weight updates or auxiliary modules. We begin by identifying a fundamental obstacle to deterministic inversion arising from zero-terminal signal-to-noise ratio (SNR) schedules and resolve it by introducing a novel noise representation, termed K-order Recursive Noise Representation. We derive a closed form expression for this representation, enabling precise and efficient alignment between the VAE-encoded and the DDIM inverted latents. To synthesize newly visible regions resulting from camera motion, we introduce Stochastic Latent Modulation, which performs visibility aware sampling over the latent space to complete occluded regions. Comprehensive experiments demonstrate that dynamic view synthesis can be effectively performed through structured latent manipulation in the noise initialization phase.

Dynamic View Synthesis as an Inverse Problem
Hidir Yesiltepe
Pinar Yanardag
hidir@vt.edu
pinary @t.edu
Virginia Tech
https://inverse- dvs g github. io/
A corgi sits on bruee beach towel. holding selfe stick with GePro
A cal weering ing Lhick round glaasen site on a deep crimeon velves ammcheir
figure against cityscope
hadmlyy men taking another figure
Figure I:
From real real-world complex scenes to AI Al-generated videos, our method preserves identity fidelity and synthesizes plausible novel views by operating entirely noise initialization phase.
Abstract
In this work, we address dynamic view synthesis from monocular videos an inverse problem in a training- free setting. By redesigning the noise initialization phase of a pre-trained video diffusion model, we enable high-fidelity dynamic view synthesis without any weight updates auxiliary modules. We begin by identifying a fundamental obstacle to deterministic inversion arising from zero- terminal signal-to to-isesee ratio (SNR) schedules and resolve it by introducing novel noise representation, termed K-order Recursive Noise Representation. We derive closed form expression for this representation, enabling precise and efficient alignment between the VAE-encoded and the DDIM inverted latents. To synthesize newly visible regions resulting from camera motion, we introduce Stochastic Latent Modulation, which performs visibility aware sampling over the latent space complete occluded regions. Comprehensive experiments demonstrate that dynamic view synthesis can be effectively performed through structured latent manipulation in the noise initialization phase.
Introduction
Dynamic view synthesis (DVS) 15
57
66 from monocular videos 12
K 30 67
65 59] is a computer vision task that aims to generate new, dynamic perspectives of scene using only single video as input. This process involves predicting how a scene would appear from angles not captured in the original footage, requiring the inference of depth, occluded regions, and unseen details. In the film industry, DVS can revolutionize post-production by enabling virtual camera sweeps through a scene producing additional shots from different angles, eliminating the need for expensive reshoots. In robotics, it supports advanced perception systems by generating synthetic
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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viewpoints that train algorithms for navigation, manipulation, and active perception tasks in complex environments.
Historically, DVS has relied on explicit 3D reconstruction methods, such as Neural Radiance Fields (NeRF) [39 its dynamic extension D-NeRF (44), K-Planes [1], and 3D/4D Gaussian Splatting 25 56]. These seminal volumetric and point-based approaches model scenes as continuous representations or point configurations. However, they impose strict prerequisites: multi-view super- vision, computationally intensive per-scene optimization, and precise camera calibration. Recently, a paradigm shift has emerged, leveraging video- diffusiinn [5]
priors to address these limitations. Diffusion models appeal for DVS because they implicitly capture geometry [64] (8] and appearance [23 63 8 62 in their latent space, inherently provide temporal consistency, and bypass the need for explicit 3D modeling. Under this diffusion paradigm, two dominant approaches have surfaced. The first involves attention-sharing architectures, as seen in Generative Camera Dolly [52), TrajectoryAAttention [59], TrajectoryCrafter [65], and ReCamMaster (2). These methods integrate camera-aware branches such as pixel-trajectory attention, dual streams, or 3D attention layers to enable fine-grained camera control. However, they require additional architectural modules and extensive retraining on large synthetic datasets like Unreal Engine 5 [10] or Kubric [16), leading to domain-gap issues when applied to natural settings. The second recipe employs LoRA-based fine-tuning, exemplified by ReCapture [67] and Reangle-A- A- Video [22]. These approaches attach spatial and temporal Low-Rank Adaptations (LoRAs) [20] 7 46
61 53
9 68 and perform per-video
fine-tuning leveraging masked losses. Across both strategies, shared limitations persist: they require updating backbone parameters adding layers, depend on curated synthetic data or vidco-specific fine-tuning, and suffer from pitfalls when the inversion process misaligns with the model's forward noise schedule. These constraints underscore critical open question: Can achieve 6-DoF monocular DVS without any weight updates, auxiliary modules, or synthetic pre-training purely by manipulating the initial noise fed into video-diffusion model?
In this work, we pioneer a fundamentally different approach to DVS from monocular videos. We demonstrate that by solely manipulating the initial noise fed into a video diffusion model, we can achieve state-of-the-ar performance without any weight updates or auxiliary modules. This novel perspective shifts the focus from architectural redesign resource-intensive retraining to efficient noise design, distinguishing our method from existing approaches. Our approach is centered around two key innovations. First, we identify and formalize the Mero-Termina SNR Collapse Problem, which arises when training schedules enforce zero signal-to-noise ratio at the terminal timestep. causing collapse in information content and obstructing deterministic inversion. To resolve this, propose the K-order Recursive Noise Representation (K-RNR), which recursively refines the initial noise in alignment with the model's 's forward schedule, enabling stable and faithful reconstruction of the original scene. We derive closed-form expressions for this refinement process and stabilize generation with an adaptive variant that prevents scale explosion. Second, to address the synthesis of newly visible content due to camera motion, we introduce Stochastic Latent Modulation, a visibility-aware sampling mechanism that directly completes occluded latent regions using context- aware latent permutations. This enables plausible scene completion in the noise initialization phase. Together, these components form unified framework that achieves figh-fidelity reconstruction and physically consistent view synthesis from monocular input. Our contributions can be summarized as follows:
We identify and formalize the Zero- Terminal SNR Collapse Problem, showing that while zero terminal SNR schedules improve generation quality, they inherently break injectivity, preventing deterministic inversion and hindering faithful reconstruction.
We propose K-order Recursive Noise Representation (K-RNR) to resolve the obstruction caused by the Zero-Terminal SNR Problem. By defining a recursive refinement relation between the VAE-encoded latent and the positive-SNR DDIM-inverted latent, we derive closed-form noise expression, enabling high-fidelity reconstructions of original scenes.
We introduce Stochastic Latent Modulation (SLM), a novel latent-space completion mecha- nism that infers content for newly visible regions by performing visibility-aware sampling and contextual latent permutation, enabling physically plausible synthesis in occluded areas without modifying the model.
2

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Original Frame
Strength: 0.88
Strength: 0.95
Dsterministic Inversion
KANN K=6
Figure 2: Approaches Kero-Terminal SNR Collapse Problem. Figures b-f shows the inpainted
versions of Figure (b) Low strength preserves source content but renders unseen regions as black. (c) High strength improves propagation into unseen areas but causes identity drift. (d) DDIM inverted latent as initial noise leads to washed-out, high saturation generation. (f) Our K-RNR (k = 6) with Stochastic Latent Modulation preserves identity and completes newly visible regions with plausible content.
2 Related Work
This section reviews prior research in two closely related areas relevant to our work. The first is novel view synthesis for dynamic scenes, and the second is video-to-video translation with camera control.
Novel View Synthesis for Dynamic Scenes. Novel view synthesis seeks to generate unseen perspectives from available visual data, with substantial advancements driven by neural rendering. For static scenes, Neural Radiance Fields (NeRF) [39] and 3D Gaussian Splatting 225] provide detailed 3D reconstructions. Dynamic scene extensions, such as D-NeRF 44) K-Planes [.. HexPlane [6]. and HyperReel M. depend on synchronized multi-view inputs, which are often impractical for casual settings. Monocular video methods, including Neural Scene Flow Fields [I], DynlBaR (32), Robust Dynamic Radiance Fields [36], and Dynamic View Synthesis [12] utilize depth-based warping or neural encodings but face challenges with occlusions and extrapolation beyond input views. Recent approaches, such 4D Gaussian Splatting (56). Dynamic Gaussian Marbles [50] and GaussianFlow [14), enhance efficiency with 3D Gaussian representations, yet require robust multi-view data significant input camera motion, restricting broader applicability.
Video-to- Video-to-Video Translation with Camera Control. Early video-to-video translation efforts, such World Consistent Video Video (37) and Few Shot Video to Video (55), targeted tasks like outpainting. Generative Camera Dolly S2 trains on synthetic multiview videos from Kubric, but domain gaps limit generalizability in natural settings. ReCapture (67] uses
stage pipeline that first generates an anchor video with CAT3D [5] multiview diffusion or point cloud rendering, followed by refinement using spatial and temporal LoRA modules. However, per video optimization hampers scalability. Methods like DaS (17 and GS DiT [3] enforce 4D consistency through 3D point tracking with tools such as SpatialTracker (58) and Cotracker 24 though tracking inaccuracies in complex scenes limit effectiveness. ReCamMaster [2) proposes generative rerendering within pre-trained trained text video models using with a frame- conditioning attention sharing mechanism using large Unreal Engine 5 [10] dataset, but struggles with high computational cost as the number of tokens are doubled in the 3D attention mechanism. TrajectoryCrafter (65) decouples view transformation and content generation using dual stream diffusion model conditioned point clouds and source videos, but remains constrained under large camera shifts. Trajectory Attention (59) applies pixel trajectory attention for camera motion control and long range consistency, however, it is sensitive to sparse or fast motions and lacks full 3D consistency.
Background
In this section, review the base video diffusion model in $3.1 followed by common noise initialization strategies used in current video models for 12V and V2V applications in $32
3.1 Base Video Diffusion Model
Following prior works 65
our work builds upon the 12V variant of the Cog [6] VideoX transformer-based video diffusion model operating latent space with a 4x temporal and x spatial compression. The model takes a single RGB image I E Hx3333 input
17
3

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Dynamic
Vidaa
DDIM Inversion
Stechastic Modulation
Loten:
Lotent
Ongiinal Video
Erignal V Vee Depth
Render Video
RNR
AdaIN
Camera Trajectory
Video Modd
Figure 3: Overview of Our Method. (Left) lift a monocular video into a dynamic 3D point cloud and render novel views under target camera trajectories, revealing unseen regions. (Right) Our method synthesizes coherent outputs by initializing noise with DDIM inversion, Stochastic Latent Modulation, and K-order Recursive Noise Representation, without modifying the video model.
and generates video V E RX with F frames. The image is first encoded by a 3D VAE (26 into a spatial latent Zing of size C H g with 16. To extend this representation across time, is broadcast along the temporal dimension and concatenated with _ 1 zero latents, forming
tensor Xo of size C x g x w Finally, X6 is concatenated with a noise tensor ~ WW I) along 8.
the channel dimension, yielding the initial noisy input Ximit of size 1 + FF-1 x 2C x H x for the
12V task.
3.2 Noise Initialization Strategies
Current video generation models 54
27 53
for Image-to- Video (12V) and Video-to- Video-to-Video
(V2V) tasks typically employ specific noise initialization strategies. These strategies can be broadly categorized into two main groups: deterministic inversion and schedule-consistent interpolation.
Deterministic Inversion. In models such as ModelScope [54] the network is conditioned on a discrete sequence of timesteps {t ...... .T. with each timestep associated with strictly positive cumulative signal coefficient ãe > 0. In this setting, the clean latent representation can be deterministically mapped to the noise manifold using DDIM Inversion
44)
Schestle-consistent Interpolation. In contrast, standard DDIM inversion is not directly applicable when the network conditioned continuous sequence of timesteps, in models like SVD (4. In such cases, the initial noisy latent is initialized as Xinit = X + y where 7y is a noise augmentation parameter that controls the strength of the initial image perturbation. In the Flow Matching- 355 video model Hunyuan Video (77. the initial noisy latent at discrete timestep E (O......7 T} given by Xisit
+ (1 (1- Xg for I2V applications. Similarly, in Wan (53), another Flow Matching model, the noise initialization is defined as X, a, + (1 ) Xg. where a, is cchedule-dependeee weighting factor. Cog 61 is trained with zero terminal signal-to-noise ratio (SNR), which makes DDIM inversion not directly applicable as we discuss in $4.1 In V2V
translation tasks, it initializes the noisy latent as Xinit Vā,Xo + vI ā,e with signal-to -onoi--to-noise-ratti åe
SNR(() I-
Methodology
Dynamic view synthesis involves simultaneously (1) preserving scene fidelity and (2) completing newly visible regions as the camera moves. This requires not only faithfully reconstructing identities and actions over time but also plausibly synthesizing previously unseen regions. To address the former, we first define the zero terminal SNR collapse problem, which reveals the incompatibility between deterministic inversion and schedule-consistem interpolation models like Cog VideoX trained with zero terminal SNR ()..1) We resolve this with K-order Recursive Noise Representation, which

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Dosine Simiartty
Expleding Meen
Exploding Variance
I:AKK Siiiiity
K-RW Mean
k-NM Std Expected
-... Expected
orddr
Korder
Figure 4: K-RNR Analysis (a) Cosine similarity between (k) and VAE-encoded latent Xo. (b) For increasing values, the mean and (c) the variance of (k)) explodes.
enables effective use of DDIM-inverted latents in such settings (.4.) To address the latter, we propose stochastic latent modulation strategy that infers unseen regions resulting from camera motion 4.4).
4.1 Zero Terminal SNR Collapse
We begin our discussion by identifying a key issue that hinders the direct use of latents during the noise initialization phase under zero-terminal SNR noise schedules. Lin et al. [34] argue that noise schedules should enforce zero SNR at the final timestep and that sampling should always start from / = T to ensure alignment between diffusion training and inference. Based on this principle,
[6]] adopts zero terminal SNR during training following the noise schedule used in [55. While this setup improves generation quality and ensures consistency between training and inference, we show that it causes a breakdown injectivity.
Proposition 4.1. Let {at) be variance- preeecccipreeeviinggg noise schedule with cumulative products a = -I (1 B,), such that the schedule enforces zero terminal SNR with āy 0. Define the forward diffusion map
@T = V + /1 âTe, ~~ I).
Then, for every pair of latents To, 2/ E Rd and every noise sample
Φ (Zo, c) = (2 = c.
Hence @T(:,c) is not injective in Fo- Consequently, deterministic inversion methods such as DDIM inversion cannot uniquely recover from
Proposition 4.1 implies that noise schedule with zero terminal SNR forces the schedule-consistent latent the last time step be
V XD + vI ÔT =; e~ IO,,
which collapses to pure noise because Ü.r = O. No information from the original frame X survives, so the resulting video-to-video translation cannot remain aligned with the source content. common workaround is to begin sampling from an earlier index < T for which a; > 0. However, it shortens the diffusion trajectory and therefore limits translation diversity, which is an important component of dynamic view synthesis. As shown in Fig 2b), this also results in the reconstruction of regions that are unseen after camera transformation. Even when ā is very small but non-zero, the stochastic term introduces perturbations that accumulate during generation and ultimately lead to identity drift as demonstrated in Fig C)..
Figure 5: Expected Norm Deviation
4.2 K-order Recursive Noise Representation (K-RNR)
Expected Norm
An alternative workaround to the zero-terminal SNR col- lapse problem is perform DDIM inversion with a posi- tive terminal SNR, allowing the resulting latent to initialize diffusion process for downstream tasks. However, as d). this approach still results in images with
Norm
shown in dd) a washed-oul appearance. We attribute this issue to mis- match between the scale of the expected initial noise and that
k-order
5

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produced by consisten interpolation, given by Xmit = V + vI- de e evaluated 0.95T. This discrepancy visualized in FigBJalong the 1 axis. Moreover, applying normalization or standardization to the Xinit introduces trajectory drift, leading to degraded results, as demonstrated in Supplementary Material.
Given the limitations of existing workarounds for the zero-terminal SNR collapse problem, we propose new noise initialization mechanism, K-order Recursive Noise Representation, which aligns deterministic inversion with schedule-consistent interpolation. In this formulation, we treat the VAE-encoded latent X as the pivol latent, and define the initial noise as Xinit = =(*) Throughout the paper, superseripts enclosed in parentheses denote recursion order, while superscripts without parentheses indicate exponentiation.
Proposition 4.2. Let X Rd be the pivot latent and let 0 denote the cumulative signal coefficient at timestep I. Define the recursive noise initialization by:
V + vI Ok
inv
and for k > 1,
ā. E( (k) vār X VI-
Then, for discrete recursion depth Nyo, the closed-form expression for (k)) is:
(R)
Σ o4 (VI
04) i-1
xn + (V1 ar) c.v.
(1)
Which can be generalized to continuous recursion depth & E R>o as:
(h) = Vāl 1 (v(Vi-a0 oz))
xo + (VT 0z) b inv
(2)
1 V1 O4.
Refer to the Appendix for the proofs of Eq. 2.. By treating Xo as a pivot latent and recursively updating the noise latent e the resulting initialization X ( becomes increasingly aligned with the structure of We quantify the alignment by measuring the cosine similarity between Xo and (k),, as shown in Fig aa). To isolate the effect of the inverted latent e we initialize the recursion with (!)) = / aa X + VI- &j e, where e ~ (O,,I), and apply the recursive formulation with discrete depth described in Proposition 4.2] As l: increases, the similarity steadily improves, indicating that K-RNR progressively enhances structural fidelity by injecting more of the original latent structure into the initialized noise.
Importantly, this growing similarity is not the only factor contributing to improved reconstruction quality. As shown Fig 5 the expected scale of c()) also becomes better aligned with the reference distribution scale as & increases, up to a certain threshold. This alignment is achieved without applying explicit normalization or standardization which results high saturation generations.
However, K-RNR on its own suffers from exploding and variance, demonstrated in Fbg/4 This indicates that as the recursion order k increases, the scale of the initialized noise grows rapidly. In practice this problem leads to high contrast outputs with exploded RGB colors in the generated video. To address this issue, we introduce Adaptive K-RNR, which stabilizes the recursion by incorporating scale information from an intermediate recursion step. Specifically, given total recursion depth k. we select an intermediate index å E (1....,k)), k). compute the intermediate noise representation c(,), and apply Xini AdaIN [c(*), c(8) This operation preserves the structural benefits K-RNR while suppressing the scale explosion that leads to visual artifacts.
Inverted Latent
Encoded Lstent
Konrder RNR
Noise
Naise
AdalN
Video Model
Figure 6: Adaptive K-RNR

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anio
Camera Transfommstion
b. Render Frame
Filled Freme
d. Generated Frame
Figure 7: Stochastic Latent Modulation Motivation. To evaluate the model's capacity for physical plausibility in unseen regions, we modify the rendered input with occlusion-filing strategies. (a) Camera motion trajectory. (b) Original render frame. (c) Occluded regions are filled by repeating background patch. (d) Resulting frame generated by combining the filled render with Giv using K-RNR, demonstrating plausible yet artifact-prone content synthesis in unseen areas.
4.3
Conditioning Camera Information
Following prior works 665 67 22 66 59 171, we incorporate explicit camera conditioning [29] into our framework to enable precise control over novel view synthesis. Given source video = [I, where each frame I, E RC*H*W we first estimate a sequence of depth maps D (D: using monocular depth prediction models, with each D, Hxx Using camera intrinsics K R333 we lift each RGB-D pair (I,, D:) into a point cloud P; R3x(H-W) via unprojection function (-), forming a dynamic point cloud sequence {P:)
P. = II II DI, K),
(3)
where II=1 denotes inverse projection from 2D image space to 3D camera space. Next, we define a set of target camera poses T (T, J where each T; E Rxx4 represents the desired relative transformation from the source view. Using these poses, we render a novel view sequence I' (T)) i= from the transformed point clouds via forward projection II(-):
r = IIT,: P, K),
where II is the standard perspective projection from 3D points to the image plane. In addition to the rendered novel views I', we generate corresponding visibility masks M' = (M] to capture occluded out-of-frame regions resulting from the camera trajectory.
4.4 Stochastic Latent Modulation (SLM)
Having addressed the fidelity aspect of dynamic view synthesis, we now turn to the second core requirement: completing regions that become newly visible as the camera moves. As shown in Fig we apply DDIM inversion to videos rendered under novel camera trajectories and interpolate between the VAE-encoded latent Xo and the DDIM-inverted latent e!"v using Adaptive K-RNR. However, regions that are occluded in the rendered input remain occluded in both X and e!",, causing these areas to be regenerated as black in the output.
To investigate this limitation, we examine whether the base model possesses meaningful physical understanding of the scene that allows it to plausibly infer content in unseen regions. We conduct an analysis on 100 randomly sampled videos from the Open Vid dataset 41, with a particular focus on cases where the input render video lies outside the training distribution violates basic physical realism. The central question is whether the model can still produce outputs that are plausible and consistent with the rules of the physical world. Although unseen areas are also encoded occluded in the inverted latent, we keep e'"h unchanged, as it retains semantic cues due to attention across visible tokens during the forward trajectory. Instead, we modify the rendered frames by experimenting with different occlusion- filling strategies. As illustrated in Fig c)), one approach involves repeating background patch across the occluded regions. When passed through the 3D VAE and combined with inv through K-RNR, this leads to plausible propagation of visual information into previously unseen areas, shown in Fig 7 d) with visible visual artifacts.
Motivated by this discovery, we propose Stochastic Latent Modulation, where instead of completing unseen regions at the input level, we perform stochastic modulation directly in the latent space. Specifically, given a binary occlusion mask M {0, 1) BxPxCXHXX where M = indicates occluded regions, and depth-based background mask D {0,1] BxxxXxxXX where D

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Original Video
Camera Transformation
C
TrijattanyAteentioon
TrijsttryCromm Croiton
DaB
FarCambir ster
Durs
Figure 8: Qualitative Comparison. K-RNR with SLM better preserves subject identity and ensures
that synthesized regions remain consistent with the original
Visual Quality
Camera Accuracy
View Synchronization
Method
FID
FVD J CLIP-T
CLIP-FT
RotEir
TransErr
Mat. Pix. (K)
FVI--V + CLIP-V
GCD
89.12
482.73
28.64
91.02
3.67
6.12
603.25
429.52
82.45
TrajectoryAttenttion
78.91
342.19
30.53
93.67
3.09
5.64
620.83
310.78
84.21
71.44
201.83
32.91
96.03
2.72
638.77
182.41
86.72
TrajectoryCrafier
62.77
162.67
34.13
2.39
823.91
108.38
88.36
ReCamMaster
58.12
118.82
35.02
98.89
1.46
4.52
863.54
82.66
89.91
Ours
53.15
103.44
35.37
98.54
1.31
4.33
881.43
75.17
92.04
Table Quantitative comparison of visual quality, camera pose accuracy, and view synchronization on 1000 randomly selected samples from the Open Vid- IM [1] dataset.
marks background areas, we define a visibility-aware sampling mask as S identifies spatial locations that both visible and lie background surfaces. We define stochastic permutation operator Ps RBxFxCxHXX - FBXXXCXXX that samples latent values from positions indicated by S and randomly redistributes them the occluded positions indicated by M. Our modulation function is given by Xo Ps Pxx)))) ب: Ps(e!") where x and are the modulated content and noise latents. This operation stochastically fills occluded regions in latent space with contextually relevant signals sampled from visible background areas, enabling the model synthesize plausible completions aligned with physical scene structure.
which
Experiments
Implementation. Our framework is built on the pretrained Cog VideoX--BBBB model. Inference is performed with 50 steps at a strength of 0.95 to ensure är > 0. For all quantitative evaluations, we set the classifier-free guidance (CFG) scale 6.0 and use recursion order of & 10 and adaptive order of = 3. 3D dynamic point clouds are generated using DepthCrafter (2I] fol- lowing the procedure described in (65). We apply DDIM inversion with positive terminal-SNN noise schedule using 30 steps, and adopt v-prediction in all cases. For quantitative evaluations, Cog VideoX's modified DDIM sampling method in the reverse trajectory. The output res- olution is fixed at 480 x 720, and all experiments are conducted on a single NVIDIA L40 GPU.
Evaluation Set. We construct dataset of 1 1100 vidcos to evaluate performance across vary- ing content and motion complexity: 1000 from Open VM 41, 50 from DAVIS 4 and 50 Al-generated videos. Open Vid-IM provides semantically rich scenes, DAVIS offers high- motion content for testing temporal stability, and Al-generated samples assess generalization to synthetic inputs. Fach video is rendered under 10 canonical camera trajectories including transla-
Method
FID 4
CLIP-T
CLIPV 1
PSNR
Noise
74.86
37.12
73.74
DDIM Inversion
102.54
19.98
63.39
5.43
K-RNR w.o AS
71.80
31.25
86.78
14.99
K RNR AS
61.43
33.46
89.12
15.64
K-RNR SLM
53.15
35.37
92.04
16.28
Figure 9: Ablation on K-RNR, Adaptive Scaling, and Stochastic Latent Modulation

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Mahoo
OpenVid
DAVIS [
Synthoic
Mran
OpenVid
H
DAVIS 33
Syntletic
Mean
OpenVid +
DAVIS [1
Systheik
Mean
GCD
0:212
0,191
0.227
0.210
0.739
0.754
0.681
0.734
TrojecoryyAtentiinn
10.11
9.70
11.04
10.28
0.241
0.211
0.272
0.241
0.685
0.708
0.61
0.670
DaS
11.37
10.14
12.27
11.26
0.309
0,290
0.345
0.305
0.586
0.621
0.545
0.584
Craffer
0.537
ReCaamMuserr
15.84
11.31
14.17
13.77
0.610
0.339
0.625
0.524
0.421
0.538
0.517
0,508
Ours
16.28
12.64
14.59
14.50
0.623
0.354
0.617
0.531
0.397
0,561
0.504
0.487
Table 2: Quantitative comparison on our curated benchmark. We report PSNR (t), SSIM (1), and
LPIPS (L), averaged over 10 canonical camera trajectories per video.
tions, pans, tilts, and arcs, to evaluate robustness under diverse viewpoint shifts.
We compare our method against five basclines: GCD [52]. PaajettoyAAtten tion [59], RecamMaster (2). TrajectoryCrafter (65). and Diffusion-as-Shatee (DaS) [7.. GCD and Trajectory are built on SVD 4 RecamMaster is based on Wan [3 while TrajectoryCrafter, DaS, and our method are based on CogVideox
Comparison Baselines.
Evaluation Metrics. We evaluate our method for camera pose accuracy, source-target synchroniza- tion, and visual quality. For camera accuracy, we use GLOMAP 42 extract estimated camera trajectories and report rotation and translation errors (RotErr, TransErr) following [8 2 Synchro- nization is measured using GIM 48 by counting matched pixels with high confidence (Mat. Pix.), along with FVD-V (60] and CLIP-V (28), which compute CLIP similarity between source and target frames at corresponding timestamps. Visual quality evaluated using FID [9). FVD (5T), CLIP-T. and CLIP-F, capturing fidelity, text alignment, and temporal consistency, respectively. We addition- ally compute the full reference metrics PSNR, SSIM, and LPIPS on the Open Vid- IM, DAVIS, and Sora-generated videos S to quantify per-frame visual fidelity with respect to ground truth frames.
Main Results. As reported in Table 0 our method achieves state-of-the-arr performance across all quantitative evaluation axes, encompassing visual fidelity, camera pose accuracy, and view synchronization. The results demonstrate that our framework consistently preserves semantic content and visual coherence while maintaining accurate geometric alignment under camera transformations. Compared to existing basclines, our approach yields improved consistency across frames and more precise reconstruction of dynamic scenes, validating the effectiveness of our noise-space formulation. Furthermore, Table Saole@rrepn reports full-reference metrics, where our method exhibits robust reconstruction quality across diverse datasets and camera trajectories, further confirming its generalizability and resilience under varying content complexity and motion dynamics. We show identity preservation quality of our method and the baselines in Fig 8 Our framework produces visually coherent results under various viewpoints and demonstrates strong temporal alignment with the source footage. For video samples, please refer to the Supplementary Material.
Ablation Studies. Table the impact of our proposed methods: K-RNR, Adaptive K-RNR. and K-RNR with Stochastic Latent Modulation. Directly using DDIM-inverted latents leads to poor results, often producing oversaturated and washed-out outputs, as seen in Fig. d). Initializing with random noise also results in weak view synchronization. In contrast, our methods significantly improve both view alignment and reconstruction quality, as reflected in PSNR and FID scores.
Noise Initialization Ablations. The results presented in Figure 10 provide a comparative eval- uation of various initialization strategies for video reconstruc- tion in the absence of camera transformations. The baseline method that begins generation with standard normal noise (c) underperforms across all metrics, which is expected due to the lack of structured guidance dur- ing synthesis. Injecting signal via a linear combination of VAE-encoded video latents (Xo) and noise, as in the Encoded Video + Random Noise strategy, yields noticeable improvements, indicating the benefit of directly in-
Method
PSNR 1
SSIM f
LPIPS
Random Noise
12.03
0.313
0.486
Encoded Video Random Noise
15.97
0.674
0.539
DDIM Inversion
9.08
0.315
0.904
Encoded Video DDIM Inversion
10.16
0.324
0.907
Random Noise + KV Caching
23.98
0.824
0.118
K-RNR
29.56
0.910
0.063
Figure 10: Ablation on noise initialization strategies for video reconstruction without camera transformation.

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corporating source video content into the initial conditions. In contrast, DDIM Inversion, which initializes with an inverted latent but without scheduler-consistens interpolation. achieves the lowest reconstruction quality, yielding high saturation, washed-out generations. The marginal improvement obtained by combining the encoded latent with DDIM inversion further underscores the sensitivity of the diffusion trajectory to initialization fidelity.
Random Noise + KV Caching introduces mechanism where the generation initiated from noise is guided by attending to key-value pairs derived from a parallel DDIM-inverted path, integrating cross-stream structural memory. This strategy shows some gains, particularly in perceptual quality as measured by LPIPS with the expense of reduced efficiency since 2 parallel attention computation over the extended sequence dimension is performed. Our proposed K-RNR approach that achieves the highest performance across all metrics, with PSNR, SSIM, and LPIPS values of 29.56, 0.910, and 0.063 respectively. These results confirm the effectiveness of recursive noise representation for high-fidelity video reconstruction. The superior quantitative outcomes suggest that K-RNR is capable of leveraging structured priors in noise space more effectively than existing baselines. Results are demonstrated in Figure 2 and corresponding videos are shared in website html
Discrete K-order Ablations. Figure II presents an ablation study on the discrete recursion depth k in K-RNR, following the application of adap- tive scaling. The results demonstrate clear per- formance trend as & increases. For shallow re- cursion depths (A: 1 and & = 2), the model exhibits poor reconstruction quality across all metrics, indicating that insufficient recursive re- finement fails to recover meaningful structure in the video content. A substantial performance jump is observed at k = 3, suggesting that min- imum level of recursive processing is necessary to capture the underlying temporal and spatial consistency required for high-fidelit generation.
K Depth
PSNR
SSIM
LPIPS +
k 1
7.82
0.221
0.896
k = 2
8.85
0.231
0.871
k = 3
15.91
0.550
0.465
1 = 4
15.94
0.550
0.468
k = 5
16.00
0,550
0.489
k 6
16.39
0.555
0.471
k 7
16.34
0.558
0.474
k 8 15.30
0.545
0.483
Figure 11: Ablation on the recursion depth k: in K-RNR after applying adaptive scaling.
As k increases beyond 3, PSNR and SSIM met- rics improve steadily. peaking at k 6 and l: 7
respectively. The LPIPS metric reaches its lowest value at k: (0.465), indicating optimal per- ceptual similarity moderate recursion depth, though values remain competitive through k = 7. Notably, performance begins to degrade at 8, likely due to over-recursion, which may introduce noise overfitting artifacts into the refinement process. These findings suggest that while increasing recursion depth generally enhances reconstruction, there exists a sweet spot around & = 6 to k = that balances iterative refinement with stability. This trade-off is essential to consider when tuning K-RNR for optimal video reconstruction performance.
6 Discussion
Limitations and Broader Impact Our method provides training-free framework for generative camera control in real-world videos, making it broadly accessible for creative editing. However, it inherits biases from the base diffusion model which may limit performance in scenes with uncommon objects, or heavy occlusion. Stochastic latent modulation can also produce unstable incoherent results when large regions become newly visible. The ability to generate realistic synthetic content raises concerns, highlighting the need for future safeguards such attribution or model auditing.
Conclusion In this paper, we introduce a training-frree framework for dynamic view synthesis from monocular videos. Our key contributions (1) the identification of the Zero-Termina SNR Collapse Problem, (2) the development of the K-order Recursive Noise Representation for the use of deterministic inversion, and (3) the Stochastic Latent Modulation technique for occlusion-awes aware scene completion. Together, they enable high-fidelity synthesis of novel views without fine-tuning or architectural changes. Through rigorous theoretical analysis and empirical validation, we demonstrate that structured manipulation of the noise space alone can unlock new capabilities in generative models, offering principled and practical path toward controllable, efficient dynamic scene generation.
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Table of Contents
Videos and Website
Symbols and Notations
Elaboration on Proposition 4.1
Forward Diffusion Map Under Zero- Terminal SNR
Breakdown Injectivity
Implications for Deterministic Inversion
Elaboration on Proposition 4.2
Proof for the Discrete Case: N >g
D.2 Proof for the Continuous Case: Rx0
Elaooration on Stochastic Latent Modulation
Technical Details of Stochastic Latent Modulation
Algorithm for Stochastic Latent Modulation
6
More Ablation Studies
Adaptive Reference Latent Index ò Ablations
6
Discussion on Quantitative Results
H
Technical Elaborations Why not set c.y 07
Parameter Settings
How To Choose k-
8
1.2 How To Choose 0?
J Proposed method on Wan 2.1 (for Flow Matching models in general)
A Videos and Website
To facilitate comprehensive evaluation and enhance result accessibility, we provide 100+ video results including motivation examples, qualitative results, ablation studies, qualitative comparisons, and limitations in our project page.
B Symbols and Notations
this section, we present the symbols and notations used throughout the paper to ensure clarity and consistency in our mathematical and algorithmic descriptions.
C Elaboration on Proposition 4.1
Consider a srriance-preserving noise schedule {az )T with cumulative products defined as ã₁ II's (1 [s), where the schedule enforces zero terminal signal-tonooise ratio (SNR), such that

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Symbol
Description
Video and Frame Symbols
Source video
L
Individual frame of the source video Sequence of depth maps Depth map for frame I Camera intrinsics matrix Point cloud for frame I; Target camera pose for frame i Rendered novel view for frame Visibility masks for novel views
D
(D
D2
K
P,
T:
M'
Latent Space Symbols
1;
Diffusion for timestep
Og
Cumulative signal coefficient at timestep
Cumulative product of a₁
Xinit
Initial noise for diffusion process
Xo
VAE-encoded latent also pivot latent
c
Noise sample from standard normal distribution
iav
DDIM inverted latent
((k)
K-order recursive noise representation
Mask and Modulation Symbols
M
Binary occlusion mask
D
Depth-based near depth mask
Visibility-aware sampling mask
Ps
Stochastic permutation operator
&
Modulated content latent
ginv
Modulated noise latent
Table 1: List of symbols used in the paper.
är 0. The forward diffusion map is given by:
Φr e) Vorua v1 ÖTE,
where E XBFxXxXX is the initial latent variable, and c NN00 I) is noise sample drawn from standard normal distribution.
C.1 Forward Diffuusin Map Under Zero-Terminal SNR
Since the zero-terminal SNR noise schedule specifies ăr = 0, substitute this into the definition of 4r:
Φ (Fo. Vārzo + /1 arr VOz, vi 0c 0 zo + +1.
Thus, ( which depends solely the noise and is independent of the initial latent zo. For any two initial latents xo, 2b E gFxcxlIX and a fixed noise sample e, it follows that:
( e) = and Dr c) e.
Therefore, P e) (r e) e, regardless of whether æo z xo + 2/6-
C.2 Breakdown of Injectivity
function A injective if. for all a, a' E A, f(a) f(a') implies a a'. Consider the map (.(e)) RFXXXHXW XFXCXHXW with fixed. From C. for any distinct zo. xi FxxXxxX where Ho * z we have:
Since (x0, = Φ t) holds even when 2o * z' the condition for injectivity is violated. Hence, ( is not injective in xo. as multiple (indeed, all) initial latents Tp map to the same output for given

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C.3 Implications for Deterministic Inversion
In diffusion models, the terminal state is denoted 27 (r c), which, under the condition âr = O, simplifies to = c. Deterministic inversion methods, such as DDIM inversion, aim to recover the original latent zo from zT by reversing the forward diffusion process. These methods assume that the forward map Φ can be inverted uniquely, which requires Φ to be injective. However, since (r(:;) <) not injective, multiple distinct #g produce the same æT = c. Consequently, given only 2r, it is impossible to determine which among the infinitely many possible initial latents was the original, rendering unique recovery via deterministic inversion unfeasible.
D Elaboration on Proposition 4.2
In this section, prove the closed-fome expressions associated with the recursive noise initialization process K-RNR outlined Proposition 4.2. The recursive process is defined as follows: for an initial step where & = 1, the expression is given by
aaro VI āye."!
and for subsequent steps where 1, the expression becomes
(k) 20 + vI- (k-1),
Here, Zo E I IF represents the pivot latent variable, 0₂ 0 denotes the cumulative signal coefficient at timestep 1, and cnvv is the initial noise term.
The proposition posits two closed-fore expressions. For the discrete recursion depth, where k E N2o. the expression is
(!k)_ Σ V (VI āt) i-1
20 + (VI az)
inv
For the continuous recursion depth, where Rzo, the expression is
(N) (Vār Vāa
(VI ④4) VT Ctt
To (VI a.) iny
The proof is divided into two parts: the discrete case addressed SD.I and continuous case is addressed in $D.2
D.1 Proof for the Discrete Case: l E Nz0
To verify the closed-form expression for discrete values of k. mathematical induction is employed as a method of proof.
For the initial step, consider the case where k = 1. The recursive definition states that
()) = /a + /I "ve!"
To confirm this, the proposed closed-form expression is evaluated at 1:
(12) Σ Vāl (VI -a)) 20 + (vI az) i
i-1
The summation involves only one term, corresponding to i 1. This term is calculated as follows:
0r (V 1 ar) 1-1 Vor. (v1 - ar)) = - Vāc.
Thus, the closed-form expression becomes
(1) Var,ro + v1 āre
which is identical the recursive definition. This establishes the validity of the expression for the base case.

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Next, suppose that for some positive integer 2 1, the closed-form expression holds true:
e
'-1 Σ V (vI -a))
01) 20 + (VI- " C.v.
The objective is now to demonstrate that this expression remains valid for the next integer, = n + According to the recursive definition,
(1+ 30 + v1 āre (n).
The inductive hypothesis substituted into this equation, yielding
(n+ = Va,to + vI- - az. Σ Voa (vI - ans) i-1
an))
xo + (VT - as)" inv
The factor v1 - Oz applied to each term within the brackets. For the summation term, this results
in
VI- ā
aa (v1 σ4
Σ
Va (vI a1)
1
and for the noise term,
vI āi (vi= (vI - (K.) n+1
Thus, the expression for (1++1) is written
(x+1) = / v0 +
Σ Val Eva (VT-aa))) xo + (VI ae) n+1 inv
The terms involving are then grouped together:
(a+1)
Voi +
n
du (VT (a)) 20 + (VI -x))
m+1 inv
i=1
To express this single summation, it is noted that v be written vau (vI az) allows the expression to be rewritten by adjusting the summation indices:
This
04
Che (VT
E 1=
Var (vT-a.))
1=1
This summation from 0 corresponds exactly the desired form when re-indexed:
(VI
Va (VI a.
since each term aligns appropriately with the change in index. Therefore, the expression becomes
(m+1))
Σ Vās (vI az) i-1 zo + (V1 - Ōe.) n+1 !nV
which matches the proposed dlosed-form expression for hypothesis for the next integer, and by the principle of mathematical induction, the closed-form expression is valid for all positive integers which completes the proof
This step confirms the inductive
D.2 Proof for the Continuous Case: & E R20
To extend the result to real values of kt the discrete case's summation analyzed as a geometric series. Let the ratio r vI ag where, given 0 a, < 1, it follows that 0 < r < 1. The summation in the discrete expression is expressed as
Σ
Ox
1=0

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The formula for the sum of a finite geometric series is applied here:
This allows the summation to be rewritten as
1 - pb
i=0
Substituting r = vI - Or back into the expression, becomes
1 (VI (x.
vā.-
Incorporating this into the discrete closed-form expression, the result is
(()) (vai 1- (vI- Zo + (v1 -a) cin
VT at
This formulation is well-defined for all real k 2 the exponential terms are continuous functions over the real numbers which completes the proof
E Elaboration on Stochastic Latent Modulation
In this section, we provide a detailed technical elaboration the Stochastic Latent Modulation (SLM) mechanism, key component of our approach to dynamic view synthesis. SLM addresses the challenge of synthesizing plausible content for regions that become newly visible due to camera motion, operating directly in the latent space of pre-trained video diffusion model. This process modulates both the VAE-encoded latent Xn and the inverted latent iav using single binary occlusion mask and depth map, ensuring a consistent and efficient strategy for handling occlusions. By leveraging visibility sampling and stochastic permutation, SLM enables the diffusion model to infer content for occluded regions without requiring architectural changes additional training.
F.1 Technical Details of Stochastic Latent Modulation
The SLM process modulates the latents x and by filling their occluded regions with values sampled from visible, depth-specific areas, using a single mask M and depth map to guide the operation. This begins with the computation of a visibility mask, defined as V = (1-M)-- (D), which identifies regions that are both visible (where M 0) and depthwise near (where D). These regions serve as the source pool for sampling, they contain stable and contextually relevant latent values from the scene. The target regions, where content synthesis is needed, correspond to the occluded areas where
M 1 1.
The modulation proceeds by identifying the spatial indices of the source and target regions. The set of source indices, Isouree consists of all positions where V = 1, while the set of target indices, Lurget, includes positions where M 1. For each latent, SI.M counts the number occluded elements (i.e., the size of Iarge)) and randomly selects an equal number of indices from Ioomne- These randomly chosen source values are then assigned to the target positions. Specifically, for x, the values at indices i Iuaget are replaced with values from randomly selected indices j Isource. such that x Xj- The same process applied to e, where Ej ej for corresponding pairs indices. This stochastic sampling ensures that the occluded regions of both latents are populated with plausible content drawn from the visible, near-depth areas of the scene.
The use of single mask and depth map for both x and ensures that the source and target regions remain consistent across the two latents, while the independent application of the sampling process to each latent preserves their distinct roles in the diffusion pipeline. The randomness in selecting source indices introduces variability, allowing the diffusion model to explore diverse completions for the occluded regions, all while maintaining coherence with the visible parts of the scene.
5

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E.2 Algorithm for Stochastic Latent Modulation
Algorithm 1 Stochastic Latent Modulation
Input:
IRBBxXCXH*X BB M {0, Bxx D RBXFXCxH*W
2: Output: Modulated x, Modulated
3: Compute visibility mask V (1 M).D
4: Let Zamare = Vi = 1
5: Let Zaaget = M =1
6: for each i Iurget do
7: Sample j ~ Uniform(Zsourc)
8: Set E; Ej
9: Set X; = Xj
10: end for
11: return X, C
More Ablation Studies
In this section, present additional ablation studies further analyze the components of approach. in F.I. we analyze the role of the adaptive normalization latent depth 5.
F1 Adaptive Reference Latent Index 6 Ablations
Figure I presents ablation study the choice of the adaptive latent index which determines the reference noise level used for adaptive malization between the k-th order noise and the set 3, and the results in this ablation empirically validate this design choice. When = 3, the model achieves the highest reconstruction qual- ity across all evaluation metries. with PSNR of 24.97, SSIM of 0.885, and LPIPS of 0.078.
8 Index
PSNR
SSIM 1
LPIPS 4
8
10.32
0.342
0.883
8 = 2
19.23
0.748
0.148
8 = 3
24.97
0.885
0.078
5-order noise. In all our experiments,
8 = 4
15.29
0.592
0,240
8
13.92
0.468
0.329
8 6
12.66
0.333
0,451
8
11.28
0.244
0.604
Figure 1: Ablation on the adaptive index 8.
Performance degrades notably when 8 deviates from this setting. For instance, lower values of such and lead to insufficient regularization, producing reconstructions with low fidelity and poor perceptual quality. Conversely, higher values of 5 (i.e., 8 2 4) introduce excessive deviation in the normalization reference, which appears destabilize the refinement process and result in less consistent outputs. This pattern suggests that 5 = 3 offers an optimal trade-off by aligning the reference noise distribution closely with the target generation stage, enabling more effective adaptive normalization. These findings confirm that careful selection of the latent reference index is critical for preserving quality in recursive refinement.
G Discussion on Quantitative Results
Table and Table 2 in the main paper present comprehensive quantitative evaluation of our frame- work against recent methods across multiple axes, including visual quality, camera pose accuracy, view synchronization, and reconstruction fidelity. The baseline methods span three architectural families: GCD and EigjectoryAAtenniinn are built upon the Stable Video Diffusson backbone, Diffu- sion as Shader (DaS) and SnjjcttoryCrfiie share the VogVideoX foundation with method, and ReCamMaster is based on the Wan architecture.
In our experiments, we observe that methods relying Stable Video Diffusion, such as GCD and Trajectory Attention, consistently underperform in preserving the identity and motion dynamics the original videos when camera transformations are introduced. This can be attributed to the limited expressiveness of the Stable Video Diffusion architecture compared to the more semantically rich representations offered by VogVideoX and Wan. Among the Cog Videoidoo-bbba based approaches, Diffusion

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Original Video Sequence
Random Noise Initialization
DDIM Inversion Reconstruction
KV Caching
Ours
Figure 2: Video Reconstruction Strategies. We perform quantitative and qualitative evaluation on video reconstruction without camera transformation application. Video results can be found in the supplementary material.
as Shader struggles to maintain action fidelity, often generating semantically coherent frames that fail reflect the intended motion trajectory. TrajectoryCrafter achieves stronger balance between action fidelity and identity preservation; however, we note that identity consistency tends to degrade toward the latter segments the video. ReCamMaster, while effective in its synthesis, incurs significant inefficiency due to its reliance on concatenating source and target video frames along the frame channel. This design increases the overall token sequence length, which not only limits scalability but also results in considerably slower inference speeds. In contrast, our proposed method retains both high fidelity and identity consistency across the video while maintaining efficient inference. The quantitative comparisons shared in website. html.

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Technical Elaborations Why not set är = 0?
Q: In experiments we use a strength of 0.95 to ensure ör > O, why not set oT 0?
When äg = 0, Equation (1) reduces to standard DDIM inversion, which is the main motivation of this paper: to demonstrate that standard DDIM inversion does not work under zero terminal SNR setting.
Let's see this situation step by step. In Equation (1), when / = T where Ür 0:
Σ ār (nrv (VI--a)) zu + (VI aT))* Einv
Σoxvi 3o + (V1)* Einy
Sinw
Thus, when â- = 0, the entire term collapses the pure noise term Eiv,, showing that image content can be reconstructed, precisely why är should remain nonzero.
Parameter Settings
I.1 How To Choose h:?
We obtained the best results when we set h = 3 and k = 6. Note that we do not tweak the & value per video-camen camera pair. We also want to clarify an important point:
Book reading example: We presented video results for k 20. This choice was made because k = 20 is optimal, but rather because it represents a relatively high value of k. Our goal that experiment to highlight the effectiveness of our adaptive normalization extension of K-RNR when l is high, which is why we chose to demonstrate the experiment a higher setting.
Monkey example: We wanted demonstrate the K-RNR's effect rendered videos with increasing values. The logic behind that experiment is demonstrating to readers the evolution of videos with different settings. As stated earlier, & generates plausible results.
Elephant and duck examples: We aimed to demonstrate the effectiveness of K-RNR in source video reconstruction when there is occlusion (i.e., SLM involved). We reported results using small values of k: [k = 2, = 3, k = 4]. to show that k = 3 is sufficient for direct video reconstruction. We will elaborate parameter selection process in detail in the camera-ready version.
I.2 How To Choose 8?
In Appendix F.3 Adaptive Reference Latent Index Ablations, conducted quantitative experi- ments regarding different values (in the table, the rows correspond to different values, while the columns vary å). In that experiment, experimental validation, we observe that the best PSNR, SSIM, and LPIPS scores are obtained when 6 3. Therefore, in all of our experiments in the main paper and supplementary videos,
report PSNR. SSIM, and LPIPS results. As result of this
8 = 3.
J Proposed method on Wan 2.1 (for Flow Matching models in general)
K-RNR, along with our dynamic view synthesis approach, directly compatible with Wan 2.1 without requiring any modifications. Furthermore, in the section below, illustrate how K-RNR

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enables us to bypass traditional iterative inversion schemes, offering a more efficient, non-iterative alternative.
In Wan noise scheduler, e' 04 + oGE operation performed, where Do the VAB-encoded latent and is sampled from standard normal distribution.
Furthermore, a₁ + 0g 1. From now on, we will use 02 = (1- - os) parameterization.
We pose the following question: How effective is K-RNR when used without relying on any inversion process?
To do so, we set e(1) = e (0, and we followed our recursive noise representation formula:
K-RNR in Flow Matching
(k) 04 (1 (t-e
When this recursion is solved, we obtain a closed-form solution again in the form of:
k ( = (1- ax + (1 - (t)
(2)
Importantly, To is sampled from the Wan 3D-VAE using argmax- argmax-sampling, which uses the mode mean of the latent distribution. Hence, E[[zo] zo and VAR[2z] = 0.
Now let's analyze the statistics and behavior of Eq. (2):
1 (1 ax)
[
Σ ((1-a))=a
a,E[vo] [1 (1 ac) B[ro]
at
(AR 2x
For the default setting, 02 = 0.07.
Behavior the mean. When 1, B[{ = 0.07E[ur). As - oo, B[eloo)] + E[zo], so gets 0.07
1 RJ 15x larger, hence exploding.
Behavior of the variance. Note that did not use inverted latents for the (1) but directly set as standard normal, different from our paper setting. This results in a completely opposite behavior when it comes to variance. As & - co, VAR[c(o)] - 0, hence it vanishing.


Reviews:
[{"review_id": "kGiIKLPJzx", "reviewer": "Reviewer_Xvr7", "summary": "The paper proposes a training-free framework for dynamic view synthesis from a single monocular video. The task is formulated as an inverse problem to structure initial noises for a pre-trained video diffusion model. The paper poses a noise representation for input reconstruction and a feature modulation technique to handle newly visible regions. Experiments show better performance than prior works.", "questions": "* SLM samples latent patches from visible background regions to fill in newly revealed areas. This implicitly assumes the background is static or, at the very least, texturally homogeneous. Has the authors attempted to extend the framework to more general settings, possibly by incorporating more priors from video models?\n* How much is the SNR collapse problem specific to CogVideoX model (or models adoptting zero terminal SNR schedules)? Does the proposed method applied to other video diffusion model backbones, e.g., Wan2.1 [1]? \n\n[1] https://github.com/Wan-Video/Wan2.1", "limitations": "Yes.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths\n* The paper frames dynamic view synthesis as a noise initialization problem for a frozen video generation model. This enables development of training-free methods. \n* Two techniques, K-RNR and SLM, are proposed to address two challenges in this task formulation, namely preserving fidelity to inputs and synthesizing unseen pixels. This is clearly presented and well motivated. \n\nWeakness\n* SLM samples from existing background regions and has inherent limitations. It may produce repetitive or semantically inconsistent results for in-the-wild videos, e.g., videos with cluttered backgrounds, or large camera movements (the latter is arguably discussed in the limitation). \n* Looking at equation (2), the variance of $\\epsilon^{(k)}$ is $(1 - \\sqrt{1 - \\bar{\\alpha}_k}^k) \\text{Var}(\\epsilon^\\text{inv})$, which should not explode (but should rather attenuate) with increasing $k$. More theoretical analysis and justifications on the empirical observation in Fig. 4 will strengthen the paper.", "was_revised": true, "final_justification": "My concerns are addressed with the additional clarifications from the authors during the rebuttal. I found this work to achieve good empirical performance, though with some missing details, e.g., how positional embeddings are handled during resampling. Including these details will help improve the paper's clarity.", "rebuttal": "## Proof | Exploding Variance\n**Q: Looking at the Eq 2 the variance should not explode. More theoretical analysis and justification on the empirical observation in Fig. 4 will strengthen the paper.**\n\nWe appreciate this insightful question. We show that indeed K-RNR variance is exploding with the increasing $k$ orders given a source video $\\mathbf{V}$. We will focus on Eq 2 to derive variance for $\\epsilon^{(k)}$. For your convenience, we rewrite Eq 2 below:\n\n$$\n\\epsilon^{(k)} =  \\sqrt{\\bar{a}_t}\\frac{1 - (\\sqrt{1 - \\bar{a}_t})^{k}}{1 - \\sqrt{1 - \\bar{a}_t}}x_0 + (\\sqrt{1 - \\bar{a}_t})^k\\epsilon^{inv}  \\tag{2}\n$$\n\nThen the variance of $\\epsilon^{(k)}$ given the source video $\\mathbf{V}$ is:\n$$\n\\text{VAR}[\\epsilon^{(k)} | \\mathbf{V}] =  \\text{VAR}[\\sqrt{\\bar{a}_t}\\frac{1 - (\\sqrt{1 - \\bar{a}_t})^{k}}{1 - \\sqrt{1 - \\bar{a}_t}}x_0 | \\mathbf{V}] + \\text{VAR}[(\\sqrt{1 - \\bar{a}_t})^k\\epsilon^{inv} | \\mathbf{V}]  \\tag{3}\n$$\n\n$$\n\\quad \\quad \\quad \\quad  =  \\left[\\sqrt{\\bar{a}_t}\\frac{1 - (\\sqrt{1 - \\bar{a}_t})^{k}}{1 - \\sqrt{1 - \\bar{a}_t}}\\right]^2\\text{VAR}[x_0 | \\mathbf{V}] + (\\sqrt{1 - \\bar{a}_t})^{2k}\\text{VAR}[\\epsilon^{inv} | \\mathbf{V}]  \\tag{4}\n$$\n\nHere it is important to remind that given the source video $\\mathbf{V}$, $\\epsilon^{inv}$ is deterministic DDIM inverted latent where stochasticity parameter $\\sigma$ is set to $0$ in the inversion process. Hence, $\\epsilon^{inv}$ is not a random variable and $\\text{VAR}[\\epsilon^{inv}] = 0$. On the other hand $x_0$ is a random variable since it is sampled from VAE using reparameterization trick with non-zero variance. \n\n**Note:** While the DDIM inversion is deterministic, mapping the source video $\\mathbf{V}$ into the VAE latent space involves sampling. To eliminate any stochasticity in this step, we use deterministic `mode sampling`, which returns the mean of the distribution with $0$ variance.\n\nThen the variance of $\\epsilon^{(k)}$ reduces to:\n$$\n\\text{VAR}[\\epsilon^{(k)} | \\mathbf{V}] =  \\left[\\sqrt{\\bar{a}_t}\\frac{1 - (\\sqrt{1 - \\bar{a}_t})^{k}}{1 - \\sqrt{1 - \\bar{a}_t}}\\right]^2\\text{VAR}[x_0 | \\mathbf{V}]  =  \\left(\\frac{\\sqrt{\\bar{a}_t}}{1 - \\sqrt{1 - \\bar{a}_t}}\\right)^2\\left[1 - (\\sqrt{1 - \\bar{a}_t})^{k}\\right]^2\\text{VAR}[x_0 | \\mathbf{V}]  \\tag{5}\n$$\n\nGiven that $\\bar{a}_t \\in (0, 1)$, we can inspect both extremes for the value of $k$. \n\n**When $k=1$:**\n$$\n\\text{VAR}[\\epsilon^{(1)} | \\mathbf{V}] = (\\sqrt{\\bar{a}_t})^2\\text{VAR}[x_0 | \\mathbf{V}] \\tag{6}\n$$\n\n**As $k \\rightarrow \\infty$:**\n$$\n\\text{VAR}[\\epsilon^{(\\infty)} | \\mathbf{V}] =  \\left(\\frac{\\sqrt{\\bar{a}_t}}{1 - \\sqrt{1 - \\bar{a}_t}}\\right)^2\\text{VAR}[x_0 | \\mathbf{V}] = \\left(\\frac{1}{1 - \\sqrt{1 - \\bar{a}_t}}\\right)^2(\\sqrt{\\bar{a}_t})^2\\text{VAR}[x_0 | \\mathbf{V}]  \\tag{7}\n$$\n\nThe quantities $\\text{VAR}[\\epsilon^{(1)} | \\mathbf{V}]$ and $\\text{VAR}[\\epsilon^{(\\infty)} | \\mathbf{V}]$ differ by the multiplicative constant $\\left(\\frac{1}{1 - \\sqrt{1 - \\bar{a}_t}}\\right)^2$ which is a very high number as $\\bar{a}_t \\in (0, 1)$. To be concrete, in our experiments $\\bar{a}_t=0.0012$. As Eq 5 is monotone increasing with respect to $k$ and we show that as limit $k \\rightarrow \\infty$ the $\\text{VAR}[\\epsilon^{(\\infty)} | \\mathbf{V}] >> \\text{VAR}[\\epsilon^{(1)} | \\mathbf{V}]$, **variance is exploding with increasing $k$.**\n\n---\n\n## Validity of SLM | How does SLM produce diverse inpaintings? \n**Q: Given that SLM resamples from visible regions to fill occluded regions, it can produces repetitive or cluttered patterns in the occluded regions./SLM assumes the background is static or, at the very least, texturally homogeneous.**\n\n* Although it may initially appear that the inpainting process simply reuses existing features potentially leading the SLM to struggle with repetitive or cluttered backgrounds, we kindly show that **this is not actually the case**. \n\n* The reason lies in the use of `positional embeddings`. Although existing features are reused for inpainting occluded regions, they are assigned different positional embeddings after the patchification process. \n\n* Specifically, **CogVideoX** adopts **3D Rotary Positional Embedding (3D RoPE)** for its relative positional encoding. In this framework, each token embedding is rotated by an angle proportional to its position. Concretely, an embedding of dimension $D$ is split into $\\frac{D}{2}$ two‑dimensional chunks. Each chunk is rotated at a different angular frequency. Lower‑dimension chunks rotate more rapidly, encoding fine‑grained positional detail, whereas higher‑dimension chunks rotate more slowly and thus retain more semantic information. As a result, the higher dimensions are less affected by the token’s position and preserve more of its semantic content [1], hence, SLM becomes a context-aware sampling mechanism.\n\n* To showcase SLM's diversity, we present a comprehensive supplementary material with 100+ diverse results. Please view Supplementary/website.html\n\n```\n[1] Barbero et al. \"Round and round we go! what makes rotary positional encodings useful?\" (2024). arXiv preprint arXiv:2410.06205. | Section 6.1 TRUNCATING THE LOWEST FREQUENCIES OF ROPE | \"Summary of the section\" part.\n```\n\n---\n\n## Proof |  Generalizability of the Zero-Terminal SNR Collapse\n**Q: How much is the SNR collapse problem specific to CogVideoX model (or models adopting zero terminal SNR schedules)?** \n\nThank you for this insightful technical question. In this section, we provide a formal proof that the identified Zero Terminal SNR Collapse is an architecture-agnostic phenomenon that arises solely due to the presence of zero terminal SNR.\n\nOur proof is based on the Maximum Entropy Principle as described in [1], specifically in **Theorem 5.6**.\n\nIn Section 4.1, we demonstrated that given two source video latents $x_0$ and $y_0$, $\\Phi_T(x_0, \\epsilon) = \\Phi_T(y_0, \\epsilon) = \\epsilon$ in the zero-terminal SNR setting which **breaks the injectivity**.\n\nFurthermore, it is known that the entropy of a random variable under deterministic transformation is always less than or equal to the original entropy:\n\n$$\n\\mathcal{H}(\\varepsilon_{\\text{inv}}) = \\mathcal{H}(\\Phi^{-1}(x_0)) \\leq \\mathcal{H}(x_0),\n$$\n\nwith equality only happens when $\\Phi^{-1}$ is one-to-one, which we showed **does not hold true**. Hence in our case:\n\n$$\n\\mathcal{H}(\\Phi^{-1}(x_0)) = \\mathcal{H}(\\varepsilon_{\\text{inv}})  < \\mathcal{H}(x_0) \\tag{1}\n$$\n\nFollowing the **Maximum Entropy Principle**, we begin by establishing an upper bound on the entropy. Our proof proceeds in two steps: \n\n1. First, we will derive this upper bound for a general random variable $Z$. \n2. We then apply the resulting inequality to the DDIM-inverted latent $\\varepsilon_{\\text{inv}}$ and the standard normal variable $\\varepsilon$ (which represents the target terminal latent in the zero-terminal SNR setting). \n\nThis comparison ultimately will show that the norm of $\\varepsilon_{\\text{inv}}$ is strictly less than that of $\\varepsilon$, hence we are obtaining the norm deviation graph in **Figure 5**.\n\nThe Maximum Entropy Principle gives the upper bound on the entropy. For a random variable $Z$ and any distribution with covariance $\\Sigma$:\n\n$$\nh(Z) \\leq \\frac{1}{2} \\log\\left((2\\pi e)^d \\det \\Sigma \\right) \n$$\n\nApplying this Maximum Entropy Principle inequality to Eq. (1) above gives:\n\n$$\n\\frac{1}{2} \\log\\left((2\\pi e)^d \\det \\text{Cov}[\\epsilon_{inv}] \\right) < \\frac{1}{2} \\log\\left((2\\pi e)^d \\det \\text{Cov}[x_0] \\right) \n$$\n\nor equivalently:\n\n$$\n\\det\\left(\\text{Cov}[\\epsilon_{inv}]\\right) < \\det\\left(\\text{Cov}[x_0]\\right) \\tag{2}\n$$\n\nReminder: Given a source video $\\mathbf{V}$, $x_0 = \\text{VAE}[\\mathbf{V}]$ which is trained to approximate multivariate Gaussian in its $d$ dimensional latent space. Hence $x_0 \\sim \\mathcal{N}(0, I_d)$. Based on this, rewriting Eq 2 gives:\n\n$$\n\\det\\left(\\text{Cov}[\\epsilon_{inv}]\\right) < \\det\\left(I_d\\right) = 1  \n$$\n\nHence every eigenvalue of $\\text{Cov}(\\varepsilon_{\\text{inv}})$ is strictly below one, and therefore:\n\n$$\n\\text{tr}(\\text{Cov}(\\varepsilon_{\\text{inv}})) < d \\tag{3}\n$$\n\nNow, we have everything to demonstrate the **expected norm deviation** formally. To demonstrate it, we will use the second moment identity of a random variable $Z$ in $R^d$:\n\n$$\n\\mathbb{E}\\left|Z\\right|^2 = \\text{tr}(\\text{Cov}[Z]) + \\mathbb{E}\\left|Z\\right|^2\n$$\n\nWhen applied to $\\varepsilon_{\\text{inv}}$ using the inequality (3), we get:\n\n$$\n\\mathbb{E} \\left\\| \\varepsilon_{\\text{inv}} \\right\\|^2 = \\text{tr}(\\text{Cov}(\\varepsilon_{\\text{inv}})) + \\mathbb{E} \\left\\| \\varepsilon_{\\text{inv}} \\right\\|^2 < d + \\mathbb{E} \\left\\| \\varepsilon_{\\text{inv}} \\right\\|^2.\n$$\n\nIn practice, $\\varepsilon_{\\text{inv}}$ is approximately centered (the network is trained with zero-mean terminal noise), giving $\\mathbb{E} \\left\\| \\varepsilon_{\\text{inv}} \\right\\|^2 \\approx 0$. This approximation is also verified in `Figure 4 (b)` where for expected noise (standard normal) norm (showed with dashes) and DDIM norm in $k=1$ axis  is in the similar scales. \n\nThus,\n\n$$\n\\mathbb{E} \\left\\| \\varepsilon_{\\text{inv}} \\right\\|^2 < d = \\mathbb{E} \\left\\| \\mathcal{N}(0, I_d) \\right\\|^2 = \\mathbb{E} \\left\\| \\varepsilon\\right\\|^2,\n$$\n\nwhich proves the claim.\n\n```\n[1] Conrad, K. (2004). Probability distributions and maximum entropy. Entropy, 6(452), 10.\n```\n\n---\n\n## Proposed methodology on Wan 2.1\n**Q: Does the proposed method applied to other video diffusion model backbones, e.g., Wan2.1?**\n\n* Our method relies on an inversion mechanism that maps a video back to the base distribution, just as DDIM inversion does in CogVideoX’s diffusion framework. In contrast, Wan is based on a flow matching model without a discrete step based reverse process, so DDIM style inversion cannot be applied directly.\n\n* Although flow models can be invertible under certain continuous normalizing flow formulations, to the best of our knowledge, to date there is no established inversion sampling procedure available for Wan."}, {"review_id": "9SoBXJJza2", "reviewer": "Reviewer_1LRA", "summary": "The paper targets on the problem of dynamic view synthesis from a monocular video. Unlike previous works doing per-scene optimization or training a multi-view diffusion model, this paper proposes a new solution paradigm which is to construct the proper noise initialization, such that an off-the-shell video model could directly generate the view synthesis results. The paper first re-project the input video into a novel view video with holes using the depth prediction. Then it proposes a dedicated method to create a noise latent as the input to the diffusion model. In its core, the paper first analyze why a naive DDIM inversion won't produce satisfactory result due to zero terminal SNR, then proposes a recursive approach to craft this noise latent using the combination of DDIM and VAE, with the help of AdaIN to rescale the latent. The experiments are carefully designed which reveals the issue of the naive DDIM inversion as well as the effectiveness of the proposed method by comparing with existing works.", "questions": "See [Major Weakness; Minor Weakness / Questions] in the above section.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strengths:\n\n1/ The idea is very interesting. As a researcher working on novel view synthesis via per-scene optimization, the proposed solution paradigm of finding the initial noise in an off-the-shell video model is very new to me.\n\n2/ The solution is intuitively reasonable, elegant and without the need of massive model training. The motivation of well presented -- the proposed K-RNR emerge from the fact that naive SSIM inversion deviates from the training distribution so we need to stay within the distribution while preserve more data information in the initialization.\n\n3/ Experiments are carefully designed to verify that the defects in the native solutions. \n\n4/ Massive results in the supplemental materials serves as proof that the proposed method works as expected comparing to the existing approaches.\n\nMajor Weakness:\n\n[Please correct me if I'm wrong. ] The only potential major weakness of the method is that it seems like the most important hyper-parameter, K, needs to be hand tweaked for different input videos: From the suppl. Videos it seems the elephant video is best recovered with K = 3, the duck one is best recovered with K=2, the monkey case seems to work the best with K=6 and the book-reading case needs K = 20. Any intuition picking K under than try-and-error?\n\nMinor Weakness / Questions:\n\nDoes it only work for foreground-background videos? Have author tried on more complex videos such as a crowd of people dancing? More over does it work with larger movement in the camera trajectory? Do you have to tweak K for different trajectory of the same video?\n\nFrom the suppl. videos, it seems TrajectoryCrafter works decently well most of the time. Hard to say the proposed method is definitely better than TrajectoryCrafter. \n\nHow to choose the intermediate index in AdaIN?", "was_revised": true, "final_justification": "I have no major concerns about this paper. All my minor concerns have been well addressed. The proposed solution is a very refreshing perspective to solve the dynamic NVS problem so I recommend for acceptance.", "rebuttal": "## How to choose $k$?\n**Q: From the suppl. Videos it seems the elephant video is best recovered with K = 3, the duck one is best recovered with K=2, the monkey case seems to work the best with K=6 and the book-reading case needs K = 20.**\n* We are thankful to reviewer for raising this practical concern. We provide additional details about our parameter selection process. Also, in `Appendix F.2: Discrete K-order Ablations section`, we conducted the quantitative experiments regarding different $k$ values. \n* **Q: Do you have to tweak K for different trajectory of the same video?** We fixed $k=10$ and $\\delta=3$ in all quantitative experiments which yields the best results.\n* **Q: Any intuition picking $k$?** We obtained the best results when we set $k=10$ and $k=6$. Note that we don't tweak the $k$ value per video-camera pair. We also want to clarify an important point:\n    * In the **book reading** example, we presented video results for $k = 20$. This choice was not made because $k = 20$ is optimal, but rather because it represents a relatively high value of $k$. Our goal in that experiment is to highlight the effectiveness of our `adaptive normalization` extension of K-RNR when $k$ is high, which is why we chose to demonstrate the experiment at a higher $k$ setting.\n    * In the **monkey** example, we wanted to demonstrate the K-RNR's effect on rendered videos with increasing $k$ values. The logic behind that experiment is demonstrating readers the `evolution of videos` with different $k$ settings. As stated earlier, $k=6$ generates plausible results.\n    * In the **elephant** and **duck** examples, we aimed to demonstrate the effectiveness of K-RNR in source video reconstruction when there is no occlusion hence, no SLM involved.  We reported results using small values of $k$: [$k = 2$, $k = 3$, $k = 4$], to show that $k = 3$ is sufficient for direct video reconstruction. We will elaborate our parameter selection process in more detail in camera ready. \n\n\n---\n\n## How to choose $\\delta$?\n**Q: How to choose the intermediate index $\\delta$ in AdaIN?** \n\n*  In `Appendix F.3 Adaptive Reference Latent Index Ablations`, we conducted the quantitative experiments regarding different  values (in the table, the rows has typo where $k$ =... needs to be  $\\delta$ = ...). In that experiment, we report PSNR, SSIM, LPIPS results. As a result of this experiment, we see that the best PSNR, SSIM and LPIPS scores are obtained when $\\delta=3$. As a result of this **experimental validation**, in all of our experiments in the paper and supplementary videos, we use $\\delta= 3$. \n\n---\n\n## Does it only work for foreground-background videos?\n\n**Q: Does it only work for foreground-background videos?** \n\n* Our work doesn't only work for foreground-background (such as `cat`, `monkey`, `book reading` examples) but also works in the presence of complex motions. Indeed, in the supplementary videos with captions `A police officer in uniform, accompanied by two men in mid-20th century overcoats and hats` and  `Two men in mid-20th century formal attire, including overcoats and fedoras, are on a boat` examples we shared two types of very complex motions:\n    * **A police officer in uniform, accompanied by two men in mid-20th century overcoats and hats |** Multiple people are walking in the original scene, moreover all of them performing diverse and very local hand gestures. We can see how K-RNR is preserving even the local hand gesture motions.\n    * **Two men in mid-20th century formal attire, including overcoats and fedoras, are on a boat |** This example is also very complex one as Di Caprio's hand movement is in slow motion and way too slower than the camera motion.\n    * Moreover, to show the effectiveness of our method in the presence of motion, different than baselines, we also shared a separate results on DAVIS dataset in the main paper.\n\n**Q: Have author tried on more complex videos such as a crowd of people dancing?**\n* Yes, we have evaluated our method on complex dancing scenes involving multiple people as requested. Specifically, we ran our model on such sequences and observed that our proposed method performs robustly even in the presence of dense, coordinated motion. Due to NeurIPS guidelines, we are not allowed to upload visuals, however these results will be added to the final manuscript. \n* We also note that our method is especially effective in cases where the source video has relatively low camera motion. In such scenarios, the video depth model (`DepthCrafter`) produces more accurate depth estimates, which in turn leads to minimal error in the 3D point cloud warping. \n* We will add more crowded, high complex motion scenes to our supplementary videos in the revised version. Specifically we will put the following complex dance scenes: \n    * The *La La Land* movie sunset dance scene (used by `ReCamMaster`), featuring a woman in a yellow dress and a man in a white shirt with a black tie.\n    * The tango scene from *Scent of a Woman* movie (used by `ReCamMaster`), set in front of a white piano, featuring a woman in a black backless dress and a man in a grey suit.\n\n---\n\n## TrajectoryCrafter vs Our Work\n**Q: From the suppl. videos, it seems TrajectoryCrafter works decently well most of the time. Hard to say the proposed method is definitely better than TrajectoryCrafter.**\n\n* Indeed, as discussed in `Appendix G. Discussion on Quantitative Results`, we elaborate our observations on TrajectoryCrafter among other methods. In particular, among the CogVideoX-based approaches, `Diffusion as Shader` struggles to maintain action fidelity, often generating semantically coherent frames that fail to reflect the intended motion trajectory. `TrajectoryCrafter` achieves a **stronger balance** between action fidelity and identity preservation; however, we note that identity consistency tends to degrade toward the latter segments of the video.  \n    * This situation can be seen in 5th comparison video where old man is lying down on a bed. \n    * We also observed empirically that when it comes to synthesizing new hand movements, our work is more plausible than TrajectoryCrafter. This situation can be seen in the 1st and 4th comparison videos.\n* Moreover, it is important to note that TrajectoryCrafter requires training a custom `Ref-DiT` module built on top of CogVideoX. This module introduces Cross-Attention between view tokens and reference video tokens, and is inserted before every DiT block in CogVideoX.\n* In contrast, our method offers a significant efficiency advantage. The proposed K-RNR + SLM solution adds **less than one second** of additional latency to CogVideoX's own inference latency, making it far more lightweight."}, {"review_id": "8WbLQ3eqQH", "reviewer": "Reviewer_gB27", "summary": "This paper addresses the challenges of dynamic view synthesis from monocular videos by introducing a training-free framework. The paper first identifies zero terminal signal-to-noise collapse problem that impedes deterministic inversion in models trained with zero terminal SNR schedules and proposes K-RNR. To further resolve the inverse problem of synthesizing newly visible regions occluded from the initial camera trajectory, the authors introduce Stochastic Latent Modulation as a mechanism to complete occluded latent regions using contextual permutations.", "questions": "1. How robust is the framework to hyperparameters $ \\delta $ and $ k $ in adaptive K-RNR? The results seem sensitive to the configuration of the adaptive component and blows up as $ k $ is increases past a small threshold. Since larger $ k $ accumulates $ x_0 $ in the weighted sum, it makes sense the values grow uncontrollably. Have you considered a weighted average to keep the norm more controlled?\n2. Have you tried approaches other than random permutation of the visible background for stochastic latent modulation? For instance, repeating the closest latent neighbor is spatially smoother than random permutations. I speculate redistributing background patches may tradeoff diversity of the generation for large occlusions especially and degrade quality as well since the latents are out-of-distribution. Initializing with pure random noise for the entirely unseen regions seem more ideal.\n3. Since the framework is training-free and based on point cloud warping, when there are large deviations from the initial camera trajectory and thus large regions become newly visible, the method can potentially produce unstable or incoherent results. How robust is the framework to challenging scenarios?", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n1. The figures are informative and comprehensive in presenting the effects of K-order noise and the ablation identifies the contribution of each component well.\n2. The underlying problem is identified and motivated clearly with concrete formalizations.\n3. Experiments are conducted across multiple datasets and baselines, validating the performance of the proposed method.\n\n**Weaknesses**\n\n1. Explicit camera conditioning section needs more elaboration. How are the camera intrinsics of videos estimated? Currently the depth maps are predicted per frame independently over the video which would result in inconsistent scales across local point clouds. How are the local point clouds registered into a consistent global point cloud? How are camera poses computed and aligned to a unified scale?\n2. Correction to CogVideoX 3D VAE latent shape. On L118, the final output shape of the latent should be $ (1 + \\lceil \\frac{F-1}{4} \\rceil) \\times 2C \\times \\frac{H}{8}  \\times \\frac{W}{8}$. The first conditioning frame is encoded independently and the rest are temporally compressed by a factor of 4.", "was_revised": true, "final_justification": "The authors have provided missing ablations and discussions that clarifies the method design and effects of hyperparameter changes. They have additionally added more context to explicit camera conditioning mechanism which was largely missing initially. Although the proposed method has novelty and experiments justify the improvements over baselines, I would like to maintain my borderline acceptance rating due to inherent limitations of training-free and point cloud warping approach. When large occluded regions become visible or errors in 3D point cloud estimation accumulate, the method produces artifacts with unstable results. These challenging cases are more practical scenarios with impactful applications.", "rebuttal": "## How robust is the framework to hyperparameters $\\delta$ and $k$ in adaptive K-RNR?\n**Q: How robust is the framework to hyperparameters $k$ and $\\delta$ in adaptive K-RNR?** \n* We thank the reviewer for this insightful question. As stated in the experiments section, we fixed $k=10$ and $\\delta=3$ in all quantitative experiments which yields the state-of-the art performance.\n* **Why $\\delta=3$:**  In `Appendix F.3 Adaptive Reference Latent Index Ablations`, we conducted the quantitative experiments regarding different  values (in the table, the rows has typo where  $k$=... needs to be  $\\delta$= ...). As a result of this experiment, we see that the best scores are obtained when $\\delta=3$ and in all of our experiments in the paper and supplementary videos, we use $\\delta= 3$. \n* **How to choose $k$?** Indeed, we obtained the best results when we set $k=6$ and $k=10$. We don't tweak the $k$ value per video-camera pair. Here we want to clarify an important ambiguity:\n\n    * In the **monkey** example, we illustrate how increasing $k$ in K-RNR affects the rendered video. The goal is to help readers observe how video content evolves with different $k$ values. As noted, $k = 6$ yields plausible results.\n\n    * In the **elephant** and **duck** examples, we demonstrate K-RNR’s effectiveness in reconstructing source videos without occlusion (and thus without SLM). We report results for small $k$ values ($k = 2$, $k = 3$, $k = 4$), showing that $k = 3$ is sufficient for direct reconstruction.\n\n    * Additionally, in `Appendix F.2: Discrete K-order Ablations`, we provide quantitative results across different $k$ values.\n\n\n---\n\n## Weighted average of $x_0$ and $\\epsilon^{(k)}$\n**Q: Have you considered a weighted average to keep the norm more controlled?** \n\nIndeed, proposing weighted average again introduces 2 parameters which may be further required to tune for each iteration in total of $k$ iterations in Equation (1). On the other hand, as discussed above, our method is quite robust when $k=10$ (or $k=6$) and $\\delta=3$ are used.\n\n---\n\n## Details on external camera conditioning\n**Q: How are the camera intrinsics of videos estimated?**\n\nOur approach employs a **fixed camera model** rather than estimating intrinsics directly from input videos, which is a common and robust practice for video-based 3D applications when camera calibration is unavailable. \n\nFollowing `TrajectoryCrafter`, we constructed the camera intrinsic matrix using **hardcoded parameters** optimized for CogVideoX video resolutions. This configuration assumes a perspective camera model with equal focal lengths in both $x$ and $y$ directions and centers the principal point appropriately for the input video dimensions.\n\n**Q: How are the local point clouds registered into a consistent global point cloud?**\n\nIndeed, we do not apply any additional registration operation for obtaining global point cloud as we already use temporally consistent depth maps extracted from `DepthCrafter`. `DepthCrafter` processes the entire video sequence as a unified input, producing depth maps that are inherently consistent across frames. \n\nIt is important to note that at the time of our submission, more advanced video depth models such as `Video Depth Anything` [1] published in CVPR 2025 were available and outperformed `DepthCrafter`. However, to ensure a fair comparison with TrajectoryCrafter, we consistently used `DepthCrafter` in all quantitative and qualitative experiments.\n\n```\n[1] Chen, Sili, et al. \"Video depth anything: Consistent depth estimation for super-long videos.\" Proceedings of the Computer Vision and Pattern Recognition Conference. 2025.\n```\n**Q: How are camera poses computed?**\n\nThe camera poses are computed in a **spherical coordinate system** where the radius parameter is automatically scaled based on the scene's depth characteristics. More specifically, we extract the depth value at the `central pixel` of the reference frame and use this as a basis for determining appropriate viewing distances. This ensures that camera trajectories are scaled proportionally to the scene geometry, maintaining consistent viewing perspectives regardless of the absolute depth values.\n\n---\n\n## Point Cloud Warping Limitations\n**Q: Since the framework is training-free and based on point cloud warping, when there are large deviations from the initial camera trajectory and thus large regions become newly visible, the method can potentially produce unstable or incoherent results.**\n\nThe reviewer is absolutely right. Indeed, as we acknowledge in our **Limitations and Broader Impact** section, stochastic latent modulation can also produce unstable or incoherent results when large regions become newly visible. To elaborate this point, we kindly note that we also qualitatively demonstrated how errors in the 3D point cloud warping can result in unpleasant results in `3D Point Cloud Rendering Artifacts` section of our supplementary videos.\n\n**Question by the Authors |** Given this limitation, why did we still choose using 3D point cloud warping as our camera conditioning mechanism?\n\nCurrently, there are two dominant ways of  camera information conditioning in the dynamic view synthesis field among methods leveraging **video diffusion priors**:\n\n* **3D point Cloud Warping:** `TrajectoryCrafter`, `Recapture`, `Reangle-a-Video`, `Viewcrafter`, `TrajectoryAttention`, `Diffusion as Shader`\n\n* **Training a camera condition embedder** `ReCamMaster`\n\nSince our method is training free, and the additional latency introduced by K-RNR + SLM on top of CogVideoX's own inference is **less than a second** on a single L40 GPU, we chose the training-free camera conditioning mechanism.\n\n**Q:  How robust is the framework to challenging scenarios?**\n\nOur framework demonstrates strong robustness across a variety of challenging scenarios. Unlike our baselines, we evaluate our method on three diverse datasets, each targeting a different robustness aspect:\n\n* **OpenVid:** This dataset includes videos of human actions involving fine-grained, local motions such as gestures and hand movements. These are particularly difficult to preserve, and our model performs well in maintaining such subtle details.\n\n* **DAVIS:**  We use this dataset to assess the robustness of our framework in the presence of significant object and camera motion.\n\n* **Sora videos:**  Beyond real-world datasets, we also test our model on source videos generated by models like Sora to evaluate robustness to synthetic content.\n\nThese evaluations collectively demonstrate that our framework generalizes well and maintains high-quality performance even under challenging or out-of-distribution conditions.\n\n---\n\n## Stochastic Latent Modulation vs other filling strategies\n\n**Q: Repeating the closest latent neighbor is spatially smoother than random permutations.**\n\nThis is an excellent observation. In fact, during our experimentation phase, the closest latent neighbor approach was the first filling strategy we explored. As the reviewer correctly notes, this method often produces smooth and visually coherent results. However, despite its strengths in generating temporally consistent outputs, we observed that in certain cases it leads to context-unaware generations.\n\nTo be concrete, in the **\"cat wearing thick round glasses sits on a crimson velvet armchair\"** source video, when we apply horizontal arc camera transformation the render video has occluded regions  behind the cat on the armchair. Using the `closest latent neighbor approach`, we consistently observed that these occluded regions were not filled with plausible continuations of the armchair. Instead, the method incorrectly filled them with textures from the background library, as if the occluded areas belonged to the library. This type of physically inconsistent hallucination was the issue that motivated us to explore alternative filling strategies and finalizing our method with a depth and context-aware stochastic latent modulation.\n\n**Q: Initializing with pure random noise for the entirely unseen regions seem more ideal.**\n\nAlthough it may initially appear that filling occluded regions with pure random noise is the simplest and more correct way, we kindly note that **this is not the case in reality**. \n\nNote that we first apply `DDIM Inversion` to obtain $\\epsilon^{inv}$, followed by our `Occlusion Filling (SLM)` step, and finally apply `K-RNR`. As a result of this transformation sequence, the proposed `Occlusion Filling` strategy must inpaint the occluded regions at the same scale as the visible ones to ensure latent consistency. \n\nHowever, it is important to emphasize that the DDIM-inverted latent $\\epsilon^{inv}$ is deterministic and does not follow a normal distribution (this situation is shown in our **Expected Norm Deviation** graph in Figure 5), since the stochasticity parameter $\\sigma = 0$ during DDIM inversion. Consequently, when we fill the occluded regions in $\\epsilon^{inv}$ with noise sampled from a normal distribution which differs in scale the resulting latent becomes out-of-distribution. This mismatch results in washed-out results again. \n\nTo match the above theory with experimental results, we conducted quantitative comparison between `noise filling` and `SLM` on 25 OpenVid examples. The results are shown below.\n\n| Method        | PSNR (↑) | SSIM (↑) | LPIPS (↓) | \n|---------------|----------|-----------|----------|\n| Noise Filling |     10.07     |  0.356         |     0.906     |\n| SLM           |    24.12      |  0.873         |    0.086      |\n\n---\n\n## Correction to 3D VAE latent shape\n**Q:  On L118, the final output shape of the latent should be** (1 + $\\lceil \\frac{F-1}{4}\\rceil \\times 2C \\times \\frac{H}{8} \\times \\frac{W}{8}$)\n\nWe thank reviewer for pointing this out. We will make sure to correct the latent shape in the camera ready version."}, {"review_id": "y9N8LoyZgU", "reviewer": "Reviewer_U62z", "summary": "This paper explores how to leverage a pretrained video diffusion model to perform novel view synthesis of dynamic scenes from monocular video input. It investigates the issue of zero-terminal SNR collapse and proposes two solutions: K-order Recursive Noise Representation (K-RNR), which preserves seen regions through effective noise initialization, and Stochastic Latent Modulation (SLM), which inpaints newly revealed regions. The work demonstrates the versatility of diffusion models in dynamic view synthesis tasks.", "questions": "I have the following concerns regarding this work, listed in order of urgency.\n\n1. **Missing relevant literature** \n   - This paper lacks sufficient discussion of related works that explore the versatile applications of diffusion models, such as the direct use of pretrained models for inpainting without fine-tuning. Although the paper builds on similar concepts, it does not adequately cite or discuss with relevant prior works, such as [1, 2].\n   - Section 4.3 of this paper bears a strong resemblance to prior work [3] presented at CVPR 2023; however, the paper does not adequately cite or discuss its relationship with [3].\n\n2. **Why not simply fix the seen regions, as done in [3]?** To make the initialization more consistent with $x_0$, this paper proposes K-RNR. Similarly, [3] suggests directly fixing the seen regions. The authors should justify why K-RNR offers advantages over the simple masking approach used in [3], either through theoretical explanation or experimental validation.\n\n3. **Overclaim.** The paper claims that their method can produce results consistent with the rules of the physical world (line 241). However, I believe this statement is overclaimed. There is no guarantee that the generated results strictly adhere to physical laws; at best, they ensure visual plausibility rather than physical accuracy.\n\n4. **I could not find relevant experiments analyzing the sensitivity of the concrete values of $k$ and $\\delta$**. How sensitive is the performance to the choice of these parameters? Do small changes in their values significantly affect the results, or is the method robust and largely insensitive across different datasets?\n\n5. **You still use a strength of 0.95 to ensure $\\bar{\\alpha}_T>0$ (line 262).** However, K-RNR is theoretically designed to overcome this limitation. Therefore, why not set $\\bar{\\alpha}_T=0$, given that K-RNR already injects information from $x_0$ into the noise? Furthermore, you discuss the drawbacks of using $\\bar{\\alpha}_T>0$ in lines 161~166. Wouldn't these limitations also apply to your method, given that you still rely on $\\bar{\\alpha}_T>0$ for noise initialization?\n\n6. **SLM Validity.** Why does randomly permuting latents in **S** into occluded regions in **M** produce coherent content? It would be valuable to see empirical comparisons between the proposed strategy and established baselines, including zero-filling, noise-filling, and content-aware approaches based on learning-free texture transfer and synthesis [4].\n\n7. **The idea presented in Proposition 4.1 appears to be intuitively straightforward.** The authors could simplify this section to shorten the presentation.\n\n8. **Typo:** At the bottom of page 8, the caption of the table incorrectly begins with \"Figure 9\", but the referenced content is a table, not a figure.\n\n\n\n[1] RePaint: Inpainting using Denoising Diffusion Probabilistic Models\n\n[2] SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations\n\n[3] RGBD2: Generative Scene Synthesis via Incremental View Inpainting using RGBD Diffusion Models\n\n[4] GIMP Resynthesizer Plugin Suite. https://github.com/bootchk/resynthesizer", "limitations": "While the paper acknowledges several limitations, it also appears that their approach relies on access to known camera trajectories in order to generate novel video content. This is challenging when camera parameters are either unknown or time-consuming to obtain.", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "**Strength**: Their method is straightforward and relatively easy to understand.\n\n**Weakness**: Although this paper was not difficult for me to read, its writing could be simplified to make it more accessible to a broader audience. For instance, the authors could use simpler terminology and provide more detailed explanations. Additionally, the experimental section lacks sufficient persuasiveness. For further limitations, please refer to the `Questions` section described later.", "was_revised": true, "final_justification": "The authors have effectively addressed all of my concerns. I believe this paper will contribute positively to the field.", "rebuttal": "## Missing Ablations | We kindly note that the requested ablations are already performed.  \n**Q4: I could not find relevant experiments analyzing the sensitivity of the concrete values of $k$ and $\\delta$**\n\nWe kindly want to inform the reviewer that we have already conducted these experiments both quantitatively and qualitatively.\n\n**Ablations of $k$ values |** In `Appendix F.2: Discrete K-order Ablations` section, we conducted the **quantitative** experiments regarding different $k$ values. We report PSNR, SSIM, LPIPS results. Moreover, we comment on the experimental results and its validity in the same section F.2. Furthermore, in our supplementary material where we share 100+ video results, the reviewer can find **qualitative** results with different $k$ values in almost **all experiments**.\n\n**Ablations of $\\delta$ values |** In `Appendix F.3 Adaptive Reference Latent Index $\\delta$ Ablations`, we  conducted the quantitative experiments regarding different $\\delta$ values (in the table, the rows has typo where $k$ =... needs to be $\\delta$ = ...). Here, we also report PSNR, SSIM, LPIPS results.  In all of our experiments in the paper and supplementary videos, we use $\\delta$ = 3. The reason for this choice is also elaborated in this section **with experimental validity**.\n\n---\n\n## Missing Experiments | We kindly note that the requested experiment is already performed.\n**Q2: Why not simply fix the seen regions?**\n\nWe kindly want to inform the reviewer that we have already conducted this experiment. \n\nIndeed, K-RNR with $k=1$ in conjunction with SLM setting directly corresponds to using original DDIM inverted latent for the seen regions and inpainting the occluded regions:\n$$\n \\text{For K=1:} \\quad \\left(\\sum_{i=1}^{k=1} \\sqrt{\\bar{a}_T}(\\sqrt{1 - a_T})^{i-1}\\right)x_0 + (\\sqrt{1 - a_T})^k\\epsilon^{inv} \\tag{1}\n$$\n$$\n = \\sqrt{\\bar{a}_T}x_0 + (\\sqrt{1 - a_T})\\epsilon^{inv} \\tag{2}\n$$\nReviewer's suggested experiment setting is comprehensively experimented qualitatively and quantitatively. In Supplementary Videos section `Noise Initialization Ablations` where we share **12 noise initialization** methods, we allocated **7 of them for this setting**: The reviewer can see clearly the evolution of the resulting dynamic views from standard DDIM Inversion to Reviewer's desired setting K-RNR with $k=1$, from recursive K-RNR starting from $k=2$ to $k=6$. The evolution of the dynamic views are very clear in these experiments.\n\n**Clarifying a potential misunderstanding:** We believe the nature of the zero-terminal SNR issue may be misunderstood, therefore we kindly provide a detailed clarification step by step:\n\n* The reviewer suggests to compare our method with [3] which fixes the seen regions using masked attention. \n* However, we kindly note that there is no need to conduct this experiment to see that it won't work. \n* The reason is that, for [3] to work in CogVideoX which is trained with zero-terminal SNR, the reviewer assumes DDIM inverted latent, when used as the initial noise directly, reconstructs the original scene in a meaningful manner.\n* Based on above assumption, it is suggested that applying masked attention to preserve the seen regions would lead to perfect reconstruction in those seen areas.\n* **However, initial assumption doesn't hold true.**  Indeed, one of the main points of our paper is showing that with zero terminal SNR the injectivity property is broken down and DDIM inverted latents reconstructs washed out results.\n    * We also kindly point out the following sections in `website.html` supporting our observations: \n        * `Zero Terminal SNR Collapse` section\n        * `Initial Noise Ablations` section \n\n---\n\n## Technical Elaborations | Why not set $\\bar{a}_T=0$?\n**Q5: You still use a strength of 0.95 to ensure $\\bar{a}_T > 0$, why not set $\\bar{a}_T=0$?**\n\nWhen $\\bar{a}_T = 0$, Equation (1) reduces to standard DDIM inversion which is the entire point of us for writing this paper: To demonstrate standard DDIM inversion does not work under zero terminal SNR setting.  \n\nLet's see this situation step by step. in Equation (1), when $t = T$  where $\\bar{a}_T = 0$, as the reviewer proposed:\n\n$$\n\\left(\\sum_{i=1}^k \\sqrt{\\bar{a}_T}(\\sqrt{1 - \\bar{a}_T})^{i-1}\\right)x_0 + (\\sqrt{1 - \\bar{a}_T})^k\\epsilon^{inv}\n$$\n\n$$\n= \\left(\\sum_{i=1}^k 0 \\times \\sqrt{1}\\right)x_0 + (\\sqrt{1})^k\\epsilon^{inv}\n$$\n$$\n = \\epsilon^{inv}\n$$\nClearly, when $t=T$ ; $\\bar{a}_T = 0$ the formulation reconstructs the standard DDIM inversion which is already shown to be problematic to directly use in regard of **norm deviation** in `Figure 5`, with its **washed out results** qualitatively shown in `Motivations`, `Approach to Zero Terminal SNR Collapse Problem`, `Noise Initialization Ablations` sections of the Supplementary Videos and **quantitatively** shown in `Figure 9`. \n\nThe entire point of K-RNR is setting VAE encoded video latent $x_0$ as the pivot latent (meaning it is fixed) and updating the standard DDIM inverted latent in our new noise formulation K-RNR as described in Line 182 in the main paper. To share information from $x_0$ and obtain a better aligned initial noise as shown in Cosine Similarity graph in Figure 4.a, we set  $t = 0.95T$ which corresponds to $a_t$ = 0.0012 in our experiments. \n\n**Wouldn't these limitations also apply to your method?** We kindly point out that we already conducted the ablation of this concern. Please refer to Supplementary Videos `Approaches to Zero Terminal SNR Collapse Problem` section to see comparison.\n\n**Additional Question |** If the reviewer's question is would K-RNR still work without shortening the diffusion path, the answer is **yes.** All of the K-RNR experiments in `Zero Terminal SNR Collapse` section in supplementary videos are conducted with $strength=1.0$ and shifting the terminal SNR. Please refer to our answer to **Reviewer zNp9** with the section name  `Easier Approach | Terminal Timestep Shifting`\n\n---\n\n## Technical Elaborations | SLM Validity\n**Q6: Why does randomly permuting latents in S into occluded regions in M produce coherent content?** \n* It is because of the positional embeddings. CogVideoX utilizes 3D Rotary Positional Embeddings (RoPE). Although already existing features are re-used for the occluded regions in SLM procedure, after patchification, these regions are rotated differently. \n* Moreover, due to the nature of RoPE, each 2-dimensional chunk of total D dimensional feature are also rotated in different frequencies. While 2-dimensional chunks in lower dimensions are rotated faster, higher dimensions are rotated slowly. \n* This means that, while lower dimensions of replaced occluded regions are being affected more by the position information, the higher dimensions are still holding the semantic information (as they rotated slower and less effected by the position information). Hence, SLM is a context aware inpainting mechanism.\n\n**Requested SLM Ablations.**\n\n| Method        | PSNR (↑) | SSIM (↑) | LPIPS (↓) | \n|---------------|----------|-----------|----------|\n| Zero Filling  |     9.16     |    0.317       |     0.911     |\n| Noise Filling |     10.07     |  0.356         |     0.906     |\n| SLM           |    24.12      |  0.873         |    0.086      |\n\nWe want to inform the reviewer that GIMP is not comparable with SLM. SLM is a purely latent space operation with channels $C=16$. GIMP, on the other hand, completely works in the image space with $C=3$\n\n---\n\n## Paper Writing | Shortening section 4.1\n**Q7: The idea presented in Proposition 4.1 appears to be intuitively straightforward.**\n\nWe thank reviewer for suggesting shorten this section. However, this section is at the heart of our method motivation.  The purpose of this section is to motivate the underlying inversion problem and demonstrating readers why $\\sqrt{\\bar{a}_T} = 0$  shouldn't be used in our K-RNR formulation. Given that there still seems to be a confusion about why we must not set  $\\sqrt{\\bar{a}_T}=0$ for high fidelity reconstruction, we will make sure to elaborate more on this section in our camera ready version. \n\n---\n\n## Paper Writing | \"The rules of the physical world\" statement\n**Q3: Overclaim.**\n\nWe used this statement in Line 241 to highlight that although physically non-plausible and non-dynamic frames are given to VAE encoder as shown in Figure 7.b, through our K-RNR formulation where $\\epsilon^{inv}$ comes from the non-filled, occluded render frames, it can generate physically plausible (we stated this way in Figure 7 caption) videos. We absolutely agree on this with the reviewer and will change the statement from \"The rules of the physical world\" to \"physically plausible\" as we mentioned in the Figure 7 caption. \n\n---\n\n## Paper Writing | Literature Review\n**Q1: Missing relative literature.**\n\n**Strong resemblance of section 4.3 to prior work |**  Indeed, section 4.3 starts with the statement \"Following prior works [58, 60, 20, 59, 55, 15] ...\" which clearly suggests that we do not propose any novel camera conditioning mechanism in this paper but rather utilize the existing, well-established mechanism by the prior works. Currently 2 ways of conditioning the camera information exists in dynamic view synthesis with video diffusion priors methods. \n\n1. Lifting each frame to 3D point cloud space, applying camera transformation and lifting down to frame space as done in:\n    * `[58] TrajectoryCrafter`  \n    * `[60] Recapture`\n    * `[20] Reangle-a-video`\n    * `[59] Viewcrafter`\n    * `[55] TrajectoryAttention`\n    * `[15] Diffusion as Shader`\n2. Training a camera condition embedder as done in:\n    * `[2] ReCamMaster`\n\nBeing a **training-free** methodology we preferred to use first camera conditioning mechanism. We thank reviewer for pointing out the original paper introducing this camera conditioning mechanism. We will make sure to cite this paper on camera-ready version.\n\n**Citing SDEdit and RePaint |** We will make sure to cite these works in camera-ready version."}, {"review_id": "EokTEArgaI", "reviewer": "Reviewer_zNp9", "summary": "This paper works on the problem of dynamic view synthesis. Different from existing works, it models this problem as an inverse problem. Specifically, it steers the pretrained video diffusion model to generate a video that matches the content that appears in the original video while hallucinating plausible content unseen in the original video. Compared to previous works, it does not require fine-tune the diffusion model.", "questions": "* My key question is regarding the motivation of K-RNR.\n  * To tackle the Zero Terminal SNR problem, there are two strategies mentioned in the paper:\n    1. Use the same zero terminal SNR noise schedule as the training time, but begin sampling at an earlier index with non-zero SNR (as mentioned in section 4.1)\n    2. Use a positive terminal SNR as mentioned in section 4.2. \n  * Does the proposed K-RNR belong to the second strategy?\n  * In my understanding, in the second strategy, the noise schedule of training and inference (i.e., for novel view synthesis) is different. Will this difference affect the performance?\n  * From the current paper, I cannot get a global understanding of the method. I suggest that the author add an algorithm figure to integrate the proposed K-RNR into the full pipeline. How does the K-RNR work with DDIM? Maybe I have some misunderstanding about the method, but I'm happy to change my mind if the author can clarify the technique details.\n  * From the experimental results, K-RNR produces good results. Can the author provide more insights on the K-RNR?", "limitations": "N/A", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "### Strengths\n* The motivation is clear. Modeling the dynamic view synthesis problem as the inverse problem is interesting.\n* The results seem of higher quality than previous methods.\n\n### Weaknesses\n* The main idea is neat. But for me, the method part is hard to follow. See the Questions section.\n* Figure 2 is not so clear.\n  * I suggest that the author add a new column to show the wrapped target view. From the current version, it is not very easy for me to figure out that bcd is the inpainted version (or the synthesized target view) of a.\n  * What is the meaning of strength? Is it the value of gamma in L129?\n* In L176, the paper mentions \"k=1 axis\" but k is not defined before.\n* I suggest the author add a comparison on runtime to compare their method with the previous methods that require fine-tuning, including the fine-tuning time and the inference time. This can help the readers better understand its benefits over the prior art", "was_revised": true, "final_justification": "All my concerns are addressed in the rebuttal. I think this paper is a valuable contribution to the community. I raise my score to weak accept.", "rebuttal": "# How to Set Terminal SNR During Inference?\n\nWe would like to clarify any ambiguities regarding our treatment of zero-terminal SNR. To ensure our approach is fully understood, we provide additional motivation behind our strategy for handling zero-terminal SNR during inference. \n\n---\n\n## Motivation | How Not To Set Terminal SNR\n\nIn this section, we focus on why the terminal SNR must not be set to $0$ in the K-RNR formulation.\n\nLet's start our motivation by analyzing K-RNR discrete formulation in Equation (1) for an extreme case: When  $t =T$ hence $\\bar{a}_T=0$.  \n\nFor your convenience, we first start by rewriting the Equation (1) here:\n\n$$\n\\left(\\sum_{i=1}^k \\sqrt{\\bar{a}_t}(\\sqrt{1 - \\bar{a}_t})^{i-1}\\right)x_0 + (\\sqrt{1 - \\bar{a}_t})^k\\epsilon^{inv}  \\tag{1}\n$$\n\nFor $t =T$ when $a_T=0$, it becomes:\n$$\n\\left(\\sum_{i=1}^k \\sqrt{\\bar{a}_T}(\\sqrt{1 - \\bar{a}_T})^{i-1}\\right)x_0 + (\\sqrt{1 - \\bar{a}_T})^k\\epsilon^{inv} \\tag{2}\n$$\n\n$$\n= \\left(\\sum_{i=1}^k 0 \\times \\sqrt{1}\\right)x_0 + (\\sqrt{1})^k\\epsilon^{inv} \n$$\n\n$$\n= \\epsilon^{inv}\n$$\nproving that, when K-RNR is used in conjunction with zero-terminal SNR noise scheduler in the inference. In conclusion, for K-RNR to get high fidelity reconstructions, the first term in Equation (1) must be non-zero:\n\n$$\n \\left\\| \\left(\\sum_{i=1}^k \\sqrt{\\bar{a}_t}(\\sqrt{1 - a_t})^{i-1}\\right)x_0\\right\\| > 0 \\tag{3}\n$$\n\nwhich is possible when terminal SNR(t) = $\\frac{\\bar{a}_t}{1-\\bar{a}_t} > 0$. This conclusion justifies again why we must use positive-terminal SNR noise scheduler in the inference.\n\n---\n\n## Technical Details | Then How To Set Terminal SNR\n**Q: Which strategy does K-RNR belong to?**\n\nAs outlined by the reviewer, there can be 2 natural approaches to obtain positive-terminal SNR given a video model trained with zero-terminal SNR. In a 50 timesteps inference setting, these approaches can be summarized as follows.\n\n### 1. Straightforward Approach | Terminal Timestep Shifting\n* In this strategy, one can shift the terminal timestep $T=999$ to an earlier timestep $T'$ where $T > T' > T-1$. In 50 timestep inference setting with uniform noise scheduler $T-1=979$. In timestep shifting strategy, **as the diffusion path is not shortened** (still 50 timesteps), the proposed framework has a lot of flexibility to both reconstruct the original layout + details and inpainting the occluded regions. \n\n**Q: Is modifying the noise scheduler affects performance?** \n\n* Timestep shifting is a valid approach as the diffusion models are trained with 1000 timesteps and know how much noise to remove in each of these 1000 timesteps. Importantly, timestep shifting approach is also adapted by the modern Diffusion DiT models and it is configurable by the users.\n* In our  experiments, only `Zero Terminal SNR Collapse` subsection under `Motivations` section in supplementary videos uses this strategy.\n\n### 2. Challenging Approach | Shortening Diffusion Steps with `strength` parameter\n\n**Q: What is the meaning of `strength` parameter in diffusion?** \n\nThe **`strength`** parameter is a inference step controlling mechanism in diffusion models which is set a ratio value between $0.0$ and $1.0$. Given a 50 timestep inference, if **`strength`** ratio is set to $1.0$, that means inference will start at terminal timestep $T=999$ and it will run for 50 timesteps: $[999, 979, 959, 939, 929 ..., 29, 19]$. When **`strength`** ratio is set to  $0.95$ the inference runs for $floor(50\\times0.95)=47$ timesteps: $[939, 929 ..., 29, 19]$. \n\n* In this strategy, the timesteps are chosen in SDEdit style with strength parameter is set to values less than 1 such as 0.95. \n* The crucial difference from this approach to terminal timestep shifting approach is that, in this strategy the **denoising path is shortened** accordingly to the chosen strength parameter.\n* This strategy sets a more challenging dynamic view synthesis environment as the video diffusion model now has less flexibility to reconstruct in high fidelity and inpaint the occluded regions.\n* This situation is demonstrated in Supplementary Videos `Approaches to Zero Terminal SNR Collapse Problem`  section with $Strength=0.95$ and $Strength=0.88$ cases.\n* In these experiments, it can be seen that: \n    * Strength=$0.88$ shortens the path more aggressively yielding results with the reconstruction of occluded regions.\n    * Strength=$0.95$ has the flexibility to inpaint a portion of the occluded region with the expense of identity drift of the monkey. \n\n### Our Approach | Hypothesis and Validity\n* As explained above, we experimented with both strategy on our end. With that, as explicitly mentioned in the `Experiments` section Line 262, we report all the results in the paper and supplementary videos except the ones under `Zero Terminal SNR Collapse` subsection (which belongs to the **first strategy**) using the **second strategy**: `Challenging Approach | Shortening Diffusion Steps ` with terminal timestep = $0.95T$ in which $\\sqrt{\\bar{a}_t} = 0.034$\n* Our hypothesis was that a better initialized noise should be able to correct the identity drift issue experienced by the baseline, furthermore it should be capable of fully completing the occluded regions plausibly. \n* Our 100+ experiments in the supplementary videos show that K-RNR accounts for original scene fidelity while SLM accounts for the propagation of the content aware information to occluded regions.\n\n---\n\n# Full Pipeline | Global Understanding of the Method\n\n**Q: From the current paper, I cannot get a global understanding of the method. I suggest that the author add an algorithm figure to integrate the proposed K-RNR into the full pipeline.**\n\nIn this section, we would like to elaborate more on global understanding of the methodology by explaining our algorithm step by step.\n\n1. Given a source video, we first apply **camera transformation**.\n    * Each frame is lifted up to 3D point cloud using depth information. \n    * Desired camera transformation is applied in point cloud space.\n    * Camera transformation applied point clouds lifted down to frame space.\n    * The resulting camera transformation applied video is called **`render`** throughout the paper and supplementary videos. \n    * Render video consists of occluded regions due to camera transformation as shown in supplementary videos. \n    * We also extract the visibility mask in this stage. Visible regions in render video are represented as 1 and occluded regions are represented as 0. \n2. Encoding render video through 3D-VAE.\n    * After VAE encoding we get the latent $x_0$. \n    * We also map depth information and binary visibility mask to CogVideoX's latent space.\n3. Applying **DDIM Inversion** to render video.\n    * A common recipe for inverting a video for high quality reconstruction in CogVideoX-5B  is using **250 forward steps inversion** [1]. \n    * However, as our K-RNR accounts for high quality fidelity we only use **20 forward steps** inversion in the inversion. \n    * As a result of inversion, we obtain inverted latent $\\epsilon^{inv}$\n4. Stochastic Latent Modulation (SLM)\n    * Based on the visibility mask and depth information, we get stochastic replacement indices for randomly replacing occluded latents.\n    * We replace occluded regions of $x_0$ based on the selected indices.\n    * We replace occluded regions of $\\epsilon^{inv}$ with the same selected indices.\n    * **Potential Question |** If the already existed visible scene features are utilized for occluded regions, how is SLM inpaints diverse, context-aware regions?\n        * It is because of the positional embeddings. CogVideoX uses 3D RoPE. Although already existing features are re-used for the occluded regions in SLM procedure these regions are rotated differently. \n        * RoPE rotates low-dimensional 2D feature chunks faster than high-dimensional ones, preserving semantics in higher dimensions and making SLM a context-aware inpainting method.\n5. K-order Recursive Noise Representation (K-RNR)\n    * After performing latent inpainting to $x_0$ and $\\epsilon^{inv}$, we perform Equation (1):\n    * $$ \\epsilon^{(k)} = \\left(\\sum_{i=1}^k \\sqrt{\\bar{a}_t}(\\sqrt{1 - \\bar{a}_t})^{i-1}\\right)x_0 + (\\sqrt{1 - \\bar{a}_t})^k\\epsilon^{inv} $$\n    * Which is followed by Adaptive Normalization:\n    * $$ \\epsilon^{(k)} = AdaIN(\\epsilon^{(k)}, \\epsilon^{(\\delta)})$$\n6. Video Diffusion Model\n    * The resulting $\\epsilon^{(k)}$ is used as initial noise.\n    * Resulting video with desired camera transformation is obtained without any modification to backbone.\n```\n[1] Yatim, Danah, Rafail Fridman, Omer Bar-Tal, and Tali Dekel. \"DynVFX: Augmenting Real Videos with Dynamic Content.\" arXiv preprint arXiv:2502.03621 (2025). | Appendix A.2.Keys and Values Extraction section.\n```\n---\n\n## Paper Writing | Figure 2 Details\n**Q: It is not very easy for me to figure out that bcd is the inpainted version (or the synthesized target view) of a.**\n\nThe reviewer is correct: Figures (b), (c), (d) are inpainted versions of (a) with different noise initialization strategies. We thank the reviewer for the suggestion and will ensure greater clarity in the camera-ready version.\n\n---\n\n## Paper Writing | $k=1$ axis statement\n**Q: The paper mentions $k=1$ axis but k is not defined before.**\n\nWe used the term \"$k = 1$ axis\" without defining it, as the graph already starts at $k = 1$, our initial condition. We thank the reviewer and will clarify this in the camera-ready version.\n\n---\n\n## Paper Writing | Adding a runtime comparison\n**Q: I suggest the author add a comparison on runtime to compare their method with the previous methods that require fine-tuning.**\n\nWe thank the reviewer for this very good suggestion, which we believe will strengthen our paper. The additional latency introduced by K-RNR + SLM on top of CogVideoX’s inference is **less than a second** on a single L40 GPU which is significantly lower than prior methods that require fine-tuning. We will include this runtime comparison in the revised version."}]

Author rebuttal:

Meta-review: This paper proposes a novel, training-free approach to dynamic novel view synthesis, offering a refreshing and promising perspective on a challenging problem. The initial reviews were mixed, with reviewers raising concerns about specific implementation details, clarity, and certain technical aspects. However, the authors provided a thorough and thoughtful rebuttal, effectively addressing all raised concerns through detailed clarifications and additional explanations.

Multiple reviewers acknowledged that their concerns were fully resolved. Reviewers broadly agreed that the method demonstrates strong empirical performance and makes a valuable contribution to the community. The Area Chair concurs with the reviewers’ final assessments and recommends acceptance. The authors are encouraged to integrate the clarifications and improvements discussed during the review process into the camera-ready version.
Decision: Accept (poster)