Dynamic View Synthesis as an Inverse Problem

Hidir Yesiltepe; Pinar Yanardag

REVIEW 3 major objections 5 minor 2 cited by

Dynamic View Synthesis as an Inverse Problem

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper shows that dynamic view synthesis reduces to editing the starting noise of a frozen video diffusion model.

desk verdict A new training-free noise-modulation recipe for dynamic view synthesis, but the state-of-the-art claim outruns the evidence. read the letter →

arxiv 2506.08004 v1 pith:7UD7APV2 submitted 2025-06-09 cs.CV cs.AI

Hidir Yesiltepe , Pinar Yanardag This is my paper

classification cs.CVcs.AI

keywords dynamicviewsynthesismonocularvideonoiseinitializationzero-terminalSNRDDIMinversiondiffusionmodelrecursiverepresentationlatentmodulation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Dynamic view synthesis (DVS) is treated here as an inverse problem in the noise initialization phase: the paper claims that a frozen video diffusion model can synthesize novel views from a single video with no weight updates, auxiliary modules, or synthetic pre-training. The obstacle is the Zero-Terminal SNR Collapse Problem: when the training schedule forces the terminal signal coefficient $\bar\alpha_T=0$, the forward map $\Phi_T(x_0,\epsilon)=\epsilon$ is not injective in $x_0$, so DDIM inversion cannot uniquely recover the source latent. The authors' fix, K-order Recursive Noise Representation, recursively mixes the VAE-encoded latent with the DDIM-inverted latent in closed form, and Adaptive K-RNR applies AdaIN to keep the scale stable. Newly visible regions are completed by Stochastic Latent Modulation, which samples visible background latents and permutes them into occlusion-masked positions. A sympathetic reader would care because, if true, camera control becomes a property of input design rather than architecture, making DVS accessible without retraining.

What carries the argument

The load-bearing object is the K-order Recursive Noise Representation, the closed-form identity $\epsilon^{(k)} = \left(\sum_{i=1}^k \sqrt{\bar\alpha_t}(\sqrt{1-\bar\alpha_t})^{i-1}\right)x_0 + (\sqrt{1-\bar\alpha_t})^{k}\epsilon_{\mathrm{inv}}$, which converts the collapsed terminal latent into a tunable mixture of source structure and inverted noise. Two auxiliary mechanisms carry the rest: Adaptive K-RNR, which applies adaptive instance normalization (AdaIN), $\mathrm{AdaIN}(\epsilon^{(k)},\epsilon^{(\delta)})$, to suppress the recursion's exploding mean and variance, and Stochastic Latent Modulation, the visibility-aware permutation operator that fills occlusion-masked latent regions by resampling visible background values. Together these replace the weight updates and camera branches of prior systems.

What would settle it

Initialize the frozen CogVideoX denoiser with the AdaIN-normalized K-RNR latent and with a standard Gaussian latent of identical mean and variance, then compare reconstruction PSNR and identity preservation: if the Gaussian latent performs as well, the recursive structure is not doing the work, and if the normalized latent is far from the training noise distribution the outputs should visibly degrade.

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Extended reading notes

Core claim

On its own terms, the paper's central discovery is that the non-injectivity induced by zero-terminal SNR is bypassable by constructing the initialization noise recursively. With the VAE-encoded latent $x_0$ as pivot, the recursion $\epsilon^{(1)}=\sqrt{\bar\alpha_t}x_0+\sqrt{1-\bar\alpha_t}\epsilon_{\mathrm{inv}}$, $\epsilon^{(k)}=\sqrt{\bar\alpha_t}x_0+\sqrt{1-\bar\alpha_t}\epsilon^{(k-1)}$ has the closed form shown in Eq. (1) and its continuous-depth generalization Eq. (2). The paper shows cosine similarity to $x_0$ rises with $k$, that the norm approaches the expected noise scale, and that the exploding mean and variance can be tamed by $\tilde{x}_{\mathrm{init}} = \mathrm{AdaIN}(\epsilon^{(k)}, \epsilon^{(\delta)})$ with $\delta=3$. It then claims that Stochastic Latent Modulation, a permutation that copies latent values from visible depth-near background locations into occluded positions, lets the frozen denoiser complete regions revealed by camera motion. The reported experiments on 1000 OpenVid videos plus DAVIS and AI-generated videos show the method ahead of GCD, TrajectoryAttention, DaS, TrajectoryCrafter, and ReCamMaster on visual quality, camera pose, and synchronization metrics.

Load-bearing premise

The method's load-bearing premise is that the recursively mixed and re-centered noise is still a plausible input for the frozen denoiser; the paper shows scale and similarity improve with recursion depth but never shows the normalized latent lies in the distribution the model was trained on.

Editorial extensions

If this is right

Any video diffusion model trained with a zero-terminal-SNR schedule becomes a candidate for training-free dynamic view synthesis, because K-RNR restores the alignment that DDIM inversion loses at $\bar\alpha_T=0$.
Since no weights change, the same frozen backbone can be reused across many camera trajectories and scenes, with only the depth estimation and noise construction recomputed per video.
The reported results imply that camera-conditioned attention branches and per-video LoRA fine-tuning are not required for competitive DVS, shifting the design space from architecture to initialization.
Adaptive K-RNR's hyperparameters matter: the ablations show quality peaking around $k=6$-$7$ and $\delta=3$ and degrading beyond them, so the gain is tied to these operating points.
If SLM generalizes, occlusion completion in DVS can be treated as a latent-sampling problem rather than an inpainting or 3D-reconstruction problem.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: because the zero-terminal-SNR collapse is schedule-level rather than model-specific, K-RNR should transfer to other diffusion models trained with the same schedule; porting it to a second backbone would be a direct test.
Editorial inference: the paper's own stated limitation that SLM can be unstable when large regions become newly visible implies the method's guarantees are regime-dependent, so large rotation or translation sweeps are the cleanest stress test.
Editorial inference: a per-video choice of $k$ could replace the fixed $k=10$ by stopping recursion when the latent norm crosses the expected Gaussian noise scale.
Editorial inference: replacing SLM's random permutation with deterministic visibility-aware inpainting in latent space would isolate whether randomness is actually needed for plausible completions.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

I'd read this one for the recipe, not for the claims. The combination of K-RNR and Stochastic Latent Modulation for training-free DVS via pure noise initialization is genuinely new, and the qualitative results are plausible. The ablations show that the recursive mixing does improve reconstruction and that SLM helps fill occluded regions. That is real, if incremental, evidence that the heuristic does something.

The theory is thin, though. Proposition 4.1 is a direct corollary of setting alpha_bar_T=0, and Proposition 4.2 is just the closed form of a geometric series. The paper presents the growing cosine similarity in Fig. 4a as an empirical discovery, but Eq. (2) makes clear that the x0 coefficient grows geometrically with k, so the alignment gain is a mathematical necessity, not a new mechanism. The stress-test point about the input distribution is fair: for large k, the x0 coefficient exceeds 1, so epsilon^(k) is no longer a plausible forward-process latent. AdaIN only matches mean and variance; it does not restore the joint distribution or the effective SNR that CogVideoX expects at timestep 0.95T. Calling this "inverse problem solving" overstates what is happening—the method is better described as injecting the source latent into the noise channel.

The empirical evaluation is the weakest part. The custom benchmark of 1100 videos with five baselines is not enough to support a state-of-the-art claim. There are no error bars, no significance tests, and no code. The two most relevant training-free baselines are missing. The hyperparameters k=10 and delta=3 are tuned on the evaluation set, and the appendix shows that k=8 degrades; that suggests the method is sensitive to tuning. The PSNR gain over ReCamMaster is 14.50 vs 13.77, which is not decisive.

To be fair, the paper is honest about limitations and the appendix contains substantial ablations. The authors seem to have a real feel for what works empirically. The central idea—redesigning the noise initialization instead of adding modules or fine-tuning—is worth exploring. But as written, the load-bearing claims are unsupported.

I would send this to a serious referee, not desk-reject it, because the direction is novel and the empirical results are non-trivially positive. But I'd expect major revision: proper comparisons, error bars, a distributional sanity check of the modulated latent, and a more measured tone. If those come through, it could be a useful paper for practitioners in video editing and camera control.

Referee Report

3 major / 5 minor

Summary. The paper proposes a training-free dynamic view synthesis method that operates entirely in the noise initialization phase of a frozen CogVideoX video diffusion model. It introduces K-order Recursive Noise Representation (K-RNR), which recursively combines the VAE-encoded latent with a DDIM-inverted latent and then applies adaptive instance normalization (AdaIN), and Stochastic Latent Modulation (SLM), which copies latent values from visible background regions into occluded regions via a random permutation. Experiments on OpenVid-1M, DAVIS, and AI-generated videos report improvements over GCD, TrajectoryAttention, DaS, TrajectoryCrafter, and ReCamMaster across visual quality, camera pose accuracy, and synchronization metrics. The paper frames the task as an inverse problem and claims that state-of-the-art performance can be achieved without weight updates or auxiliary modules.

Significance. If the central claim held, the paper would demonstrate that novel-view synthesis can be repurposed from a frozen video diffusion model by only manipulating initial noise, which is practically attractive and conceptually interesting. The paper includes formal propositions with proofs in the appendix, a broad set of baselines, and both full-reference and no-reference metrics. However, the core mechanism reduces to injecting the encoded latent into the noise channel, and the reported gains are not tied to a demonstrated inverse-problem solution. The evaluation lacks error bars, code, and an isolated assessment of newly visible regions, so the significance is currently below what the paper claims.

major comments (3)

[§4.2, Eq. (2)] The closed-form expression in Eq. (2) shows that the coefficient of x0 is sqrt(ᾱ_t) * (1 - (sqrt(1-ᾱ_t))^k) / (1 - sqrt(1-ᾱ_t)), which grows with k and tends to a limit strictly larger than 1 as k→∞. Therefore the monotone increase in cosine similarity reported in Fig. 4(a) is a mathematical consequence of the recursion, not an empirical demonstration that the initialization is 'aligned' in a way that supports inverse problem solving. More importantly, at t=0.95T the frozen denoiser was trained on inputs with signal coefficient sqrt(ᾱ_t) < 1; substituting a latent whose signal component is amplified beyond this coefficient induces a train/test distribution shift. The paper provides no distributional or manifold-level evidence that AdaIN(ε^(k), ε^(δ)) lies in the support of inputs the denoiser expects at that timestep. The observed reconstruction gains may therefore reflect source-signal leakage rather than a valid solution to an inverse problem.
[§4.4, Algorithm 1] SLM fills occluded latent regions by randomly copying values from visible, depth-near background positions. This is an ad-hoc stochastic permutation without any guarantee of spatial or temporal coherence; indeed, the limitations paragraph in §6 acknowledges that SLM 'can produce unstable or incoherent results when large regions become newly visible.' The quantitative evaluation does not isolate the quality of the completed regions: PSNR/SSIM/LPIPS in Table 2 are computed against ground-truth frames that do not contain ground truth for out-of-view content, so those numbers mostly reflect reconstruction of the already-visible content. A per-region or no-reference evaluation of newly synthesized areas is required before the claim of 'physically plausible synthesis in occluded areas' is supported.
[Tables 1-2 and §5 (Implementation)] The central state-of-the-art claim is supported only by point estimates without error bars or significance tests. The hyperparameters k=10 and δ=3 are selected using the same evaluation set on which the ablations in Appendix E.2 and E.3 are performed, so the reported comparisons are at risk of selection bias. The baselines also rest on different base models (SVD, Wan, and CogVideoX), and no code or detailed evaluation protocol is released, making it difficult to verify that the comparisons are controlled. Reporting variance across seeds and trajectories and releasing code would be necessary to support the headline claim.

minor comments (5)

[Appendix E.3] The title 'δblations' is a typo; it should be 'δ ablations'.
[§3.2] The notation '¯at' in the SNR formula 'SNR(t) = ¯at/(1−¯at)' should be 'ᾱ_t' with a subscript t for consistency with the rest of the paper.
[Main text, Ablation Studies] The text refers to 'Table 9' for the ablation results, but the ablation table is embedded in a figure environment ('Figure 9: Ablation on K-RNR...'), making the cross-reference inconsistent.
[§4.2, Adaptive K-RNR] The use of AdaIN is described only as matching mean and variance; a citation to the original adaptive instance normalization work (e.g., Huang and Belongie, 2017) and a short explanation of why these statistics are the relevant ones would improve clarity.
[§5, Implementation] The paper fixes the CFG scale at 6.0 but does not report sensitivity to this choice; given that CFG is known to interact strongly with noise initialization, a brief sensitivity analysis would aid reproducibility.

Circularity Check

2 steps flagged · score 6.0 of 10

K-RNR's alignment measure is tautological and the Table 2 full-reference metrics compare against the same rendered views that are fed in as conditioning input, so the main evaluation partly reduces to reconstruction of the input render.

self definitional [Section 4.2, Proposition 4.2 and Fig. 4(a)]
"By treating x0 as a pivot latent and recursively updating the noise latent ϵ(i), the resulting initialization xinit = ϵ(k) becomes increasingly aligned with the structure of x0. We quantify the alignment by measuring the cosine similarity between x0 and ϵ(k), as shown in Fig.4(a)."

Equation (1) defines ϵ(k) = (∑_{i=1}^k √¯αt(√1−¯αt)^{i−1}) x0 + (√1−¯αt)^k ϵinv. The coefficient multiplying x0 is a finite geometric series that strictly increases with k, while the ϵinv coefficient decays geometrically. Therefore the growing cosine similarity reported in Fig.4(a) is a direct consequence of the definition of ϵ(k), not an empirical discovery. The sentence 'K-RNR progressively enhances structural fidelity by injecting more of the original latent structure into the initialized noise' restates the construction: more x0 is injected by the recursion by construction, so measuring alignment with x0 cannot validate the method.
fitted input called prediction [Section 4.4 and Section 5 (Evaluation Set and Table 2)]
"we apply DDIM inversion to videos rendered under novel camera trajectories and interpolate between the VAE-encoded latent x0 and the DDIM-inverted latent ϵinv using Adaptive K-RNR ... Each video is rendered under 10 canonical camera trajectories ... We report PSNR (↑), SSIM (↑), and LPIPS (↓), averaged over 10 canonical camera trajectories per video."

The pipeline consumes the rendered novel view as its conditioning signal: that render is VAE-encoded into x0 (the K-RNR pivot) and DDIM-inverted into ϵinv. Table 2 then scores the generated video against the same canonical-trajectory renders as 'ground truth' via PSNR/SSIM/LPIPS. The target frames are therefore part of the model's input before they are 'predicted.' High full-reference scores mostly certify that the frozen denoiser reproduces the conditioning render, not that it synthesizes genuinely unseen geometry or content. The central claim of state-of-the-art dynamic view synthesis is accordingly supported by a metric that reduces, by construction, to reconstruction of the input render.

full rationale

The paper's mathematical derivation of the closed form (geometric series) is self-contained and correct; no load-bearing self-citation chain appears (the paper cites external baselines and builds on CogVideoX). However, two internal reductions compromise the claimed validation. First, the cosine-similarity growth in Fig. 4(a) is an arithmetic consequence of Eq. (1), which explicitly injects an increasing amount of x0 into ϵ(k); the paper presents this as evidence of progressive alignment. Second, the full-reference benchmark feeds the rendered novel view into the diffusion model as the conditioning latent and then scores against those same rendered views, so Table 2's PSNR/SSIM/LPIPS measure copy fidelity of the input render rather than novel-view inference. These are specific reductions visible from the paper's own equations and protocol, not author-intent speculation. The method still contains independent components (e.g., stochastic latent modulation) and Table 1 reports distributional metrics that are not literally the same input-as-target reduction, so the circularity is partial rather than total.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

No new physical entities are introduced; K-RNR and SLM are algorithmic constructs defined on existing latents, so they do not raise the graviton-problem concern. The free parameters are the recursion depth, the adaptive reference index, the inversion strength, the CFG scale, the number of inversion steps, and the unspecified depth threshold.

free parameters (6)

timestep t / strength = t = 0.95T (strength 0.95)
Chosen as a hyperparameter for DDIM inversion and initialization; the paper says inference is performed with strength 0.95 to ensure alpha_bar_T > 0 (Section 5), but no principled selection is given.
recursion depth k = k = 10
Selected in implementation; ablation E.2 shows performance peaks near k=6-7 and degrades at k=8, making k=10 a post hoc choice.
adaptive reference index delta = delta = 3
Selected by ablation E.3 where delta=3 gives best PSNR/SSIM/LPIPS; this is the reference latent used in AdaIN.
CFG scale = 6.0
Standard classifier-free guidance scale, set in implementation; not fitted to the method but affects all quantitative results.
number of DDIM inversion steps = 30
Implementation detail affecting the inverted latent; chosen by hand.
depth-based background mask D threshold = not specified
The paper defines D as a 'depth-based background mask' (Section 4.4) but never states the threshold used to binarize depth; this affects SLM sampling.

assumptions (5)

domain assumption CogVideoX is a sufficient pretrained video diffusion prior for DVS
The whole framework assumes the frozen model can synthesize plausible novel views and complete occluded regions when initialized with K-RNR/SLM latents (Sections 3.1, 4.4). No proof or analysis beyond qualitative results.
domain assumption The zero-terminal SNR schedule with alpha_bar_T=0 is the actual training schedule of CogVideoX
The argument in Proposition 4.1 depends on this premise (Section 4.1, citing [57,41]); if the schedule differs, the collapse problem and the entire motivation change.
ad hoc to paper Randomly copying latent values from visible background into occluded regions produces contextually plausible content
SLM's permutation PS is motivated by an experiment in Fig. 7, but no theoretical or statistical justification is given (Section 4.4).
domain assumption The depth map and visibility masks are reliable
The unprojection, rendering, and SLM all rely on DepthCrafter depth estimates and derived masks (Section 4.3); errors in depth directly corrupt the rendered novel views and the source pool for latent sampling.
standard math The closed-form geometric series is a valid continuous extension for real k
Appendix C.2 extends the discrete sum to real k using the geometric series formula; this is standard math, but the continuous interpretation of 'recursion depth' is not physically meaningful.

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Cite this review

Pith. "Pith review of Dynamic View Synthesis as an Inverse Problem." pith.science (2026). https://pith.science/paper/7UD7APV2

@misc{pith2026250608004,
  author       = {Pith},
  title        = {Pith review of: Dynamic View Synthesis as an Inverse Problem},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7UD7APV2}},
  note         = {Machine review of arXiv:2506.08004}
}

read the original 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.

Figures

Figures reproduced from arXiv: 2506.08004 by the authors.

**Figure 2.** Approaches to Zero-Terminal SNR Collapse Problem. (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… view at source ↗

**Figure 3.** Overview of Our Method. (Left) We 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 K-order Recursive Noise Representation, and Stochastic Latent Modulation without modifying the video model. into a spatial latent zimg of size C × H 8 × W 8 , with C = 16. To… view at source ↗

Figures from the paper (10 more)

**Figure 4.** Figure 4: K-RNR Analysis (a) Cosine similarity between ϵ (k) and VAE-encoded latent x0. (b) For increasing k values, the mean and (c) the variance of ϵ (k) explodes. propose a stochastic latent modulation strategy that infers unseen regions resulting from camera motion (§4.4). 4…

**Figure 5.** Figure 5: Expected Norm Deviation 1 5 10 15 20 25 30 35 40 45 50 k-order 600 800 1000 1200 1400 1600 L2 Norm Expected Norm k-RNR Norm An alternative workaround to the zero-terminal SNR collapse problem is to perform DDIM inversion with a positive terminal SNR, allowing the res…

**Figure 6.** Figure 6: Adaptive K-RNR However, K-RNR on its own suffers from exploding mean and variance, as demonstrated in Fig.4(b–c). 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 o…

**Figure 7.** 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-filling strategies. (a) Camera motion trajectory. (b) Original render frame. (c) Occluded regions are fill…

**Figure 8.** Figure 8: Qualitative Comparison. K-RNR with SLM better preserves subject identity and ensures that synthesized regions remain consistent with the original scene. Method Visual Quality Camera Accuracy View Synchronization FID ↓ FVD ↓ CLIP-T ↑ CLIP-F ↑ RotErr ↓ TransErr ↓ Mat. Pi…

**Figure 9.** Figure 9: Ablation on K-RNR, Adaptive Scaling, and Stochastic Latent Modulation Evaluation Set. We construct a dataset of 1100 videos to evaluate performance across varying content and motion complexity: 1000 from OpenVid-1M [36], 50 from DAVIS [38], and 50 AI-generated videos.…

**Figure 1.** Figure 1: Ablation on noise initialization strategies for video [PITH_FULL_IMAGE:figures/full_fig_p019_1.png]

**Figure 2.** Figure 2: Ablation on the recursion depth k in K-RNR with after applying adaptive scaling [PITH_FULL_IMAGE:figures/full_fig_p019_2.png]

**Figure 3.** Figure 3: Ablation on the adaptive reference latent [PITH_FULL_IMAGE:figures/full_fig_p020_3.png]

**Figure 4.** Figure 4: 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. 8 [PITH_FULL_IMAGE:figures/full_fig_p021_4.png]

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Forward citations

Cited by 2 Pith papers

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