Walking the Schrödinger Bridge: A Direct Trajectory for Text-to-3D Generation
Authors: Ziying Li
Xuequan Lu
Xinkui Zhao
Guanjie Cheng
Shuiguang Deng
Jianwei Yin
Venue: NeurIPS 2025 poster ()
Keywords: Generative Models
Text-to-3D
3D Gaussian Splatting
Diffusion Models
Primary area: deep_learning

Abstract: Recent advancements in optimization-based text-to-3D generation heavily rely on distilling knowledge from pre-trained text-to-image diffusion models using techniques like Score Distillation Sampling (SDS), which often introduce artifacts such as over-saturation and over-smoothing into the generated 3D assets. In this paper, we address this essential problem by formulating the generation process as learning an optimal, direct transport trajectory between the distribution of the current rendering and the desired target distribution, thereby enabling high-quality generation with smaller Classifier-free Guidance (CFG) values. At first, we theoretically establish SDS as a simplified instance of the Schrödinger Bridge framework. We prove that SDS employs the reverse process of an Schrödinger Bridge, which, under specific conditions (e.g., a Gaussian noise as one end), collapses to SDS's score function of the pre-trained diffusion model. Based upon this, we introduce Trajectory-Centric Distillation (TraCe), a novel text-to-3D generation framework, which reformulates the mathematically trackable framework of Schrödinger Bridge to explicitly construct a diffusion bridge from the current rendering to its text-conditioned, denoised target, and trains a LoRA-adapted model on this trajectory's score dynamics for robust 3D optimization. Comprehensive experiments demonstrate that TraCe consistently achieves superior quality and fidelity to state-of-the-art techniques. Our code will be released to the community.

Walking the Schrödinger Bridge: A Direct Trajectory for Text-to-3D Generation
Ziying Li Zhejiang University emmal eeezzju edu. en
Xuequan Lu University of Western Australia edu. au
Xinkui Zhao" Zhejiang University chaoxinkui0zji edu, cn
Guanjie Cheng Zhejiang University
Shuiguang Deng Zhejiang University dengagōzju. edu. edu. en
Jianwei Yin Zhejiang University zjuyjи@cs zju
beeegguanjieezjuu edu.
zju.edu.cc. edu.
https://github. http://b...oo//mmaaaaee//////eae
VSD, CPG 7.5
SDS, CFG
100
VSD, CFG 20
SDS, CFG 20
Ours, CFG -
Figure 1: From left to right: (a) Standard VSD [45] (CFG=7.5 CFG: Classifier-free Guidance); (b) Standard SDS [35]; (CFG 100); (c) VSD [45] (CFG = 20); (d) SDS [35] (CFG 20); (e) Ours (CFG = 20). VSD with CFG 7.5 and CFG 20 both yield low-quality results. Standard SDS yields artifacts (e.g., over-smoothing) with high CFG, and SDS with low CFG yields low-quality results.
Our method generates high-quality and high-fidelity results with fair CFG value.
Abstract
Recent advancements in optimization- based text-to-3I) generation heavily rely on distilling knowledge from pre-trained text-to-image diffusion models using techniques like Score Distillation Sampling (SDS), which often introduce artifacts such as over-saturation and over-smoothing into the generated 3D assets. In this paper, we address this essential problem by formulating the generation process as learning an optimal, direct transport trajectory between the distribution the current rendering and the desired target distribution. thereby enabling high- quality generation with smaller Classifier-f free Guidance (CFG) values. At first, theoretically establish SDS simplified instance of the Schrödinger Bridge framework. We prove that SDS employs the reverse process an Schrödinger
"Corresponding author, maaxxinkui@zju..oo www...uu.uuuurr... cn
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Bridge, which, under specific conditions (e.g., a Gaussian noise as one end), collapses to SDS's score function of the pre-trained diffusion model. Based upon this, we introduce Trajectory-Cennt -Centric Distillation (TraCe), novel text-to-3D generation framework, which reformulates the mathematically trackable framework of Schrödinger Bridge to explicitly construct diffusion bridge from the current rendering to its texl-conditioned, denoised target, and trains a LoRA-adapted model on this trajectory's s score dynamics for robust 3D optimization. Comprehensive experiments demonstrate that TraCe consistently achieves superior quality and fidelity to state-of- the-art techniques.
Introduction
Generating three-dimensional content directly from textual descriptions has recently attracted inten- sive attentions in the research community. Recent methods leveraging explicit 3D representations like Gaussian Splatting have significantly accelerated the generation process [25, 3]. Despite the advancements, it remains a key bottleneck that the quality and fidelity of generated 3D assets often lag behind their 2D counterparts. This limitation is frequently attributed to the scarcity of large-scale, high-quality 3D datasets required for direct supervised training [27, 28, 10].
To bridge this gap, many ofite-of-theaasd art text-to-3D methods employ optimization strategies guided by powerful. pre-trained 2D text-to-image (T2I) diffusion models [36]. Score Distillation Sampling (SDS) [35] has become the cornerstone paradigms. SDS leverages powerful pre-trained 2D text- to-image diffusion models to guide the optimization of 3D representations. Nevertheless, the standard SDS approach typically requires high values for Classifier-Free Guidance (CFG) [13] to achieve strong text alignment [35, 47, 4, 24, 49]. This reliance on high CFG values is often problematic, leading to visual artifacts such as over-saturation [37] and over-smoothing [23] in the generated 3D assets. Recognizing these issues, several variants of SDS have been proposed recently [45, 29, 17, 44, 48, 11, 6]. However, these SDD-basedd methods, including the recent variants, face persistent challenges. Firstly, as analyzed in recent studies [45, 1, 24], SDS and its variants fundamentally operate by matching the gradient direction predicted by the T2I model. While differing in their specific source and target choices for computing this gradient, they all rely on score estimates derived from the T21 backbone. These score estimates, however, can be noisy and are not guaranteed to represent an optimal direction for 3D optimization (shown in Figure 2b), potentially causing unexpected artifacts. Secondly, variants designed to operate effectively lower CFG values (e.g., CFG=7.5), such as Score Distillation via Inversion (SDI) [29] or Variational Score Distillation (VSD) [45], have shown limited success when applied optimizing certain popular 3D representations like 3D Gaussian Splatting (3DGS), often yielding less-desired results (shown in Figure 1).
The aforementioned analysis underscores the limitations of existing approaches and highlights the urgent need of a more robust optimization framework for text-to-3D generation, one that does not solely rely on potentially noisy score matching or operate under restrictive guidance conditions. In this paper, we first provide a theoretical insight by establishing that SDS can be understood as a simplified instance of the Schrödinger Bridge framework [39]. We demonstrate (Section 4. that SDS implicitly employs the reverse process of an Schrödinger Bridge, which, under specific conditions such as Gaussian noise distribution at one endpoint, effectively collapses to utilizing the score function of the pre-trained diffusion model. This perspective not only clarifies the underlying dynamics of SDS but also illuminates pathways for more principled trajectory design. Based upon this reformulation, we introduce Trajectory-Cent formulates the mathematically tractable framework of Schrödinger Bridges [26, 26] to explicitly construct and learn a diffusion bridge for text-to-3D generation. This bridge connects the current rendering (X₂) to its text-conditioned, denoised target (XXpred), ), thereby defining a more stable and direct optimization trajectory (visualization in Figure 2a). TraCe then employs Low-Rank Adaptation (LoRA) [14] to fine-tune the T2I diffusion model specifically for navigating this constructed bridge, enabling it to precisely learn the score dynamics required for robust 3D optimization along this optimal trajectory towards the target distribution.
Distillation (TraCe), a novel text-to-3D generation framework. TraCe
Our proposed TraCe framework, which operationalizes the direct transport path via Schrödinger Bridges, is rigorously evaluated. Extensive experiments demonstrate that this approach yields high- fidelity 3D assets with strong adherence to textual descriptions (Figure 4 and Table 1). The results consistently showcase TraCe's capacity to achieve superior visual quality and semantic coherence

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in generated content (Figure 4 and Supplementary), highlighting the efficacy of our theoretically grounded direct trajectory optimization for text-to-3D generation.
In summary, our contributions are:
We establish a novel theoretical connection, demonstrating that SDS can be precisely under- stood as a special case of the Schrödinger Bridge framework. This reformulation clarifies the underlying transport dynamics implicitly leveraged by SDS.
We introduce Trajectory-Centric Distillation (TraCe), new text-to-3D generation framework. TraCe explicitly learns an optimal transport path, guided by a tractable Schrödinger Bridge formulation, between the current 3D model's rendering and a dynamically estimated, text- aligned target view. This is achieved by constructing and sampling along this explicit diffusion bridge, enabling more direct and stable 3D optimization.
Experiments demonstrate that TraCe achieves high-quality 3D generation, surpassing current state-of-the-art techniques. TraCe exhibits enhanced robustness, particularly excelling in challenging low CFG values where the performance of existing methods typically degrades.
2 Related Work
Distilling 2D into 3D. Leveraging large-scale, pre-trained text-to-image (T2I) diffusion models [36] as priors has become prominent technique for generation tasks in data-scarce domains, such as text-to-3D generation. SDS [35] is seminal approach in this direction, enabling optimization of parametric representations (e.g.. Neural Radiance Fields) by distilling knowledge from 2D diffusion model. To achieve plausible results, frequently necessitates high Classifier-Free Guidance (CFG) weights [35, 47], which can further exacerbate these issues. However, standard SDS is often susceptible to visual artifacts such as over-saturation [37] and over-smoothing [23]. Moreover, the SDS objective itself, while empirically effective, does not strictly correspond to the gradient of a well- defined probability distribution of the 3D parameters [45, 1, 24J, potentially leading to suboptimal optimization paths [17, 44, 29, 48]. To address these limitations, several variants have been proposed. For instance, methods like Variational Score Distillation (VSD) [45] and Classifier Score Distillation (CSD) [48] explore alternative gradient formulations to better approximate the optimization process from source distribution towards target distribution. Other approaches like Score Distillation via Inversion (SDI) [29] tries better approximate the noise instead of using pure Gaussian noise. These variants can be understood through the lens of approximating an optimal transport path between the current image distribution (source) and the target natural image distribution, and from this perspective, a key difference between these methods lies in how they approximate the score of the source and target distributions [30]. For instance, SDS approximates it using the unconditional score, while VSD attempts more direct approximation by fine-tuning LoRA adapter on the current renderings. While these methods offer valuable contributions towards reducing the source distribution mismatch artifacts, they fundamentally rely on adapting gradients derived from pre-trained T2I models. This forces the optimization process to cope with score functions optimized for 2D image generation, which is inherently not optimal for tasks like 3D generation due to the domain gap and differences. Our work differs greatly from these approaches. We establish a novel theoretical connection, demonstrating that SDS can be precisely understood as specific instantiation of the Schrödinger Bridge framework. This reformulation clarifies the underlying transport dynamics implicitly leveraged by SDS. Built upon this insight, we introduce a method that explicitly constructs and learns more direct and stable optimization trajectory by framing the process as a tractable Schrödinger Bridge between the current rendering and an estimated text-aligned target, thereby enhancing both the fidelity and robustness of text-to-3D generation.
Diffusion Models and Schrödinger Bridges. Diffusion models (DMs) [12], also known as Score- based Generative Models (SGMs) [40, 42], have emerged as a dominant class of deep generative techniques, achieving state-of-the-an performance in synthesizing high-fidelity data across various domains, notably images [40, 12, 42, 9]. These models typically define forward diffusion process, often formulated as a stochastic differential equation (SDE), that gradually corrupts data samples into simple prior distribution, usually Gaussian noise. A neural network is then trained, often via score-matching objectives [16, 43, 42), to approximate the score function (gradient of the log density) of the perturbed data distributions. This learned score function parameterizes reverse-time
3

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Annall
0.
6-
D22
Fonde
(a)
(b)
Figure Left: Schrödinger Bridge Visualization and Samples. Top: Probability flow of the bridge from current rendering (Fmddr to the predicted target (ore distribution. Bottom: Corresponding image samples, showing the current rendering, intermediate bridge samples (x:)), and the final predicted target. Right: Gradient and Intermediate Rendering Comparison. The first row shows TraCe gradients, the second shows SDS gradients, and the third shows rendered images of the 3D models that have not finished generation. Note the reduced artifacts and potentially more coherent structure in the TraCe gradients and intermediate renderings.
SDE that transforms samples from the prior back into data samples. While being extremely success- ful, this standard paradigm typically relies on initiating the generative process from unstructured noise. The Schrödinger Bridge problem provides more general theoretical framework, originating from statistical physics [38, 39] and connected to entropy-regularized optimal transport [21, 5] and stochastic control [7, 34J. aims find the most likely stochastic evolution between two specified arbitrary distributions, PA and Pn. rather than being restricted to a noise prior. This offers the potential learn direct transformations between complex data manifolds. Attempts have been made to apply Schrödinger Bridge concepts to text-to-3D generation. For instance, [30] proposes naive approach to direct Schrödinger Bridge formulation between current renderings and target images guided by text prompts, though this requires an initial stage involving standard SDS. Another approach, DreamFlow [20], proposes to approximate the backward Schrödinger Bridge dynamics between current renderings and target images by simply repurposing fine-tuned text-to-image model, heuristic potentially deviating from the true underlying Schrödinger Bridge process. We critically advance text-to-3D generation by establishing the precise theoretical relationship between SDS and Schrödinger Bridges. This foundational insight is then exploited develop a principled methodology for direct distributional transport, enabling the construction of trajectories towards text-aligned target distributions.
3 Preliminaries
Score-based Generative Model (SGM) and Schrödinger Bridge. Score-based Generative Models (SGM) [40, 42] learn to generate data by reversing a predefined forward diffusion process. This process gradually transforms data Xo PA into noise X1 ~ .N(0,) I) and is often governed by forward stochastic differential equation (SDE). Generation then proceeds by simulating the corresponding reverse- time SDE [2], starting from X, and integrating backward to t 0. The forward and reverse SDEs are given by:
dX, = d(( + g.dW, (forward)
dx, = [f((),) V log p(,,() dt - gidW, (backward)
Here, W, (and W,) is standard Wiener process, and 9: represents the time-dependent diffusion coefficient. The central part of this reversal is the score function Vx, log p(Xe, which is unknown and approximated using a time-conditioned neural network (X,, 1) (or an equivalent noise predictor (x,,X,,)) ()). This network is trained using score-matching objectives [43, 42] pairs (Xo, X,) sampled from the forward process. Sampling is performed by numerically integrating the reverse SDE using solvers like DDPM [12] DDIM [41].

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The Schrödinger Bridge problem [39, 21] offers a generalization of SGMs to learn nonlinear diffusion processes between two arbitrary distributions, Xg PAA and X1 Ps. seeks the most likely stochastic evolution connecting these boundary distributions, described by a pair of forward and backward SDEs:
dX, [fi(X)) B.V d) VBdWW, (forward)
dx, = - - (x,, at + VB,WW, (backward)
where (a () and (2x,), 1) are non-negative functions known Schrödinger factors, determined by coupled partial differential equations with boundary conditions (2x, 0) (xx, 0) = PA(x)) and (x, (x, 1) = pz The forward and backward processes induce the same marginal density q(r, t) at any time E [0, 11, satisfying Nelson's duality (ax (z) t) - g(z, t) [33]. Notably, SGM is a special case where ps = (0, I) and (xx t) R causing the forward drift modification to vanish and V (z. 1) Rs g(x, 1), recovering the score function in the reverse SDE.
Score Distillation Sampling (SDS). Score Distillation Sampling (SDS) [35] enables generating 3D assets by leveraging powerful pre-trained 2D text-to-image diffusion models [36]. bypassing the need for large-scale 3D datasets. It optimizes the parameters 0 of differentiable 3D representation, such as NeRF [31]. InstamtNGP [32], or 3D Gaussian Splatting (3DGS) [18], using gradients derived from the diffusion model. In this work, adopt 3DGS primarily for its rapid generation capabilities and high-fidelity visual output.
The core mechanism of SDS involves repeatedly rendering the 3D model from different views (I = 900 c)), adding noise to the rendering ztt), and using the 2D diffusion model's score estimate (denoising prediction éprca) to guide the optimization of O. Formally, the gradient is computed as
VeLSDS Er,,, (o(t) (Fpree Cnoise)
(1)
where w(() is a weighting factor and the term (Epred - Enoiso) provides the guidance signal. While SDS can be intuitively understood as moving renderings towards higher-density regions according to the 2D prior or formally interpreted via probability density distillation, the exact nature of its gradient signal is debated [17, 48, 44, 1, 45]. Practically, SDS often requires high lassifier-free guidance (CFG) values, which can sometimes lead to artifacts like oversaturation or blur [17, 29, 46, 19, 37, 22]. Furthermore, the strategies that employ lower CFG values, for instance, methods explored in text-to- NeRF [45, 29], have demonstrated limitations when directly applied to the generation of 3D assets with Gaussian Splatting (Figure 4). Recent efforts such as LueidDreamer [23] have investigated text-to-3DGS under low CFG conditions: however, this direction currently faces trade-offs, including prolonged optimization durations (over 5000 iterations) and limitations in the attainable visual quality (Figure 4). Our work builds upon SDS by mitigating these issues through deriving more direct and tractable optimization path, formulating Schrödinger Bridges guide the generation process for achieving greater fidelity with lower CFG values.
4 Method
The preceding analysis of existing methods like Score Distillation Sampling (SDS) raise a natural question: can a principled framework be developed define a direct, optimal transformation trajectory where both its source and target ends are explicitly and robustly aligned with the desired true distributions? Addressing this challenge-by establishing explicit control over the distributional endpoints of the generative trajectory, rather than relying on unstructured priors (e.g., a Gaussian noise)-is crucial for enhancing the fidelity and control of generative outcomes. To this end, we exploit the theoretical underpinnings of the Schrödinger Bridge problem, particularly its tractable formulations [26, 8], which provide a robust mechanism for learning direct, optimal transport paths between specified distributions. Our methodological contribution unfolds in two stages: first, we theoretically establish that standard SDS is indeed special case of the Schrödinger Bridge framework, thereby providing new perspective on its operation (Section 4.1.. Second, building upon this insight, we propose a novel optimization algorithm grounded in tractable Schrödinger Bridge principles, to achieve improved distributional alignment throughout the generative process (Section 4.2).
5

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<11
Proepts
Cyean
Randon
Sumpling
Updaae
(1Cr B.t.. 1069
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Figure 3: Overview of Strajectory-Centric Distillation (TraCe). Our TraCe optimizes 3D parame-
ters by computing a distillation gradient with a LoRA-adapted 2D diffusion model, Eg. Given a text prompt y and camera parameters (1) the current 3D model is rendered in random view to produce Tmnr- (2) An ideal target view zi aipeed estimated from Zindr using a pre-trained diffusion model pretmiin via one-step denoising. (3) An intermediate latent 2y is sampled from the analytic bridge posterior q(Ze | =a -mmdrt) at time t. (4) The LoRA model predicts the noise for 2t, and the difference between this prediction and the target noise is computed. (5) This difference directs the calculation of the TraCe gradient V WTlCee and drives the update of LoRA parameters Φb
4.1 Score Distillation Sampling as a Special Case of Schrödinger Bridges
In this section, we reformulate the SDS objective by examining its core guidance principles, and show it employs simplified form of the backward dynamics found in the Schrödinger Bridge framework.
As established in Section Score-based Generative Model (SGM) aligns with special configura- tion of the Schrödinger Bridge problem. This occurs when the Schrödinger Bridge's distribution Pи t=== = 1 Gaussian noise (P/ (O, 7)) and its forward Schrödinger factor (xx, t) 1. Under these conditions, the term 9: V x. log Y (X,, f)) in the forward Schrödinger Bridge SDE vanishes, causing the forward Schrödinger Bridge dynamics become identical the SGM's standard diffu- sion process. Consequently, the marginal densities g(Xe,() () of this particular Schrödinger Bridge are equivalent to the SGM's s noisy marginals p(,,,)).
The crucial step in linking the Schrödinger Bridge and reMerve reverse processes from score perspective lies in Nelson's 's duality, Ti (X,, f) (X,, t) = q(X,, t). Given (XX,, t) = 1 and g(X,,t) t) = p(X,, for this specific Schrödinger Bridge, the duality simplifies to:
1 (X,, R p(x,0) = (xx,,))x((X
(2)
This directly implies that the score term in the general Schrödinger Bridge backward SDE, -Vx, log (X,, t), becomes - Vx, log p(X,,t). This is precisely the score approximated by the leamned network (X,, t) (or its equivalent noise predictor e(X,, t)) in SGM.
SDS utilizes this learned score su (X,,)) from pre-trained SGM to guide the optimization of differentiable generator g()). The update for (0) is fundamentally derived from (X,, t). aiming make the generated samples xo = g() consistent with the data manifold learned by the SGM.
Therefore, from a score gradient perspective:
SDS operates using the score function (x,,,, learned by an SGM.
The derivation above shows that (X,,), (approximating Vx, log,(X,, t)) is equivalent to the score - Vx, log (Xe, t) of a Schrödinger Bridge under the specific conditions that reduce the Schrödinger Bridge to SGM.
Remark. essence, SDS leverages score gradient that is equivalent the score function governing the reverse dynamics of the canonical Schrödinger Bridge implicit in any SGM. While general Schrödinger Bridges can offer more complex dynamics, SDS employs the score from this specific, simplified Schrödinger Bridge structure. Thus, the SDS mechanism represents application of principles governing special case of Schrödinger Bridges, distinguished by its reliance on the SGM-derived score Sp.

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4.2 Traajectoy--enttrcc Distillation
To optimize the 3D model parameters such that current renderings Emdr = g(0, c) align with a target text description y, we propose novel method, namely Trajectory-Centrcc Distillation (TraCe). This method leverages a 2D diffusion model, adapted with LoRA parameters denoted as Eg. to provide guiding gradient V VoLrrac.(0) The core idea is conceptualize diffusion bridge between the current rendering and an estimated ideal target image.
Constructing the Diffuusio Bridge for Trajectory Guidance. At each optimization step for 0, we construct a specific diffusion bridge instance defined by two endpoints:
1. Initial Bridge Endpoint (X1 + T:ndt): The current rendering F'dr = g(t, c) serves as the starting point of the reverse diffusion trajectory aim to learn. In the context of our bridge, this is treated as the "noisier" state at bridge time / =
2. Target Bridge Endpoint (Xg f xbb prod An estimated ideal target view s0 pro acts as the desired endpoint bridge time t 0. This target is dynamically obtained by performing one-step denoising on Frddr using a pre-trained texl-to-image model Epretmin [20], conditioned on the text prompt y: T0 (Irddr
v1 Oxf' (pecrrin (mndes t' v)) /vor, where dy is from the noise
schedule of (pretrain-
With these two endpoints, =/pe and Tmur, established, we then sample an intermediate latent state along the conceptual bridge. For a sampled time t [0.02, 0.5], following the tractable formulation of Schrödinger Bridges [26], Iz is drawn from the analytically known conditional distribution
I ( .mdrr Nix: M4, Σ,I), where the mean f Po
pred + (1 =nd is an
/ +o)) is the bridge variance. The coefficient 7t- = of/ (a} + ot), and of fh 3,dT, oj = J 8r are accumulated variances from noise schedule 3e specific to this bridge construction. This 2a represents a state on direct trajectory from =/ pood being progressively "noised" towards Tinde (or equivalently, Xnnd being progressively "denoised" towards u.pe along this trajectory).
interpolation between the target image and current rendering, and E, = of
Optimizing 0 via the Bridge Trajectory. We then optimize 0 using the LoRA-adapted model Co(are f, 1,y,c) c), which is trained to predict the noise that would take o; towards x .rpred The objective for 8 utilizes co to measure the consistency of xe with respect to Jyndr along this bridge:
VoLince Ee,,.c w(l) (co(vrn1.,,))
Frnde 0r
Durprrd (Imdrr t, v) Oxs Or,
ax 00
U-net Jacobian
where Findd = g(0, c). L ~ (0(002,, 0.5). and is the text prompt. The term Ie is sampled from q(xz pgge mmdr) defined above, and or V d, from the bridge's noise schedule. Following the convention of SDS, we omit the U-Net Jacobian term (Qeget (...) Oz
+ 1) for effective training,
as it can be treated learnable or constant factor absorbed by w(t). Thus, we have:
VeLTrace = E.,,,o uu(() (co( (,, Et
Fmdr
00
Scheduled t-Sampling for Schrödinger Bridges Interpolation. For sampling the intermediate
state in our TraCe objective (Eq. (4)), which dictates the characteristics of x; ~ g(0; x .mndr), we adopt a t-annealing strategy, similar the approach proposed in [15]. Throughout the optimization of 0, the time parameter t is progressively decreased from an initial value near 0.5 towards 0.02. This common annealing technique gradually shifts the focus of the Schrödinger Bridge interpolation from broader states towards those more proximate to the estimated ideal target z aiding the progressive refinement of the rendered output g(0,c) c).
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Experiments
SDS
SDS
Our
hermel crab wiihe colorfid shel!
golden goblet,
CSD
Ours
CSD
Ours
f
Azcomee our DSLR photo as anigurus motorgrale
VSD
Qur
VSD
Ours
car mude out of subii
large, mutti-loyyred, nywneiica woildnng zooochh foualnnt piping, and liellle sugar flowers ia full bloom displayed on stlvr stand Qurs
SDI
Ous
SDI
blue inhute
rosk turley
plates
ISM
Qurs
ISM
Qurs
violin
Figure 4: Qualitative comparisons. We present visual examples with the same text prompt.
Implementation Details. We choose recent state-of-the-art (SOTA) text-to-3D approaches for comparison:
NeRF-based methods, such as Classifier Score Distillation (CSD) [48], ProlificDreamer (VSD) [45], and Score Distillation via Inversion (SDI) [29], and 3DGS- bos-d methods like Gaus- sianDreamer (SDS) [47] and LucidDreamer (ISM) [23]. Please see more details and experiments in Supplementary.
Qualitative Comparisons. Figure presents visual results for several challenging text prompts. Our approach demonstrates the ability to generate higher quality 3D assets compared to other SOTA methods. Compared SDI [29]. our method yields significantly improved texture fidelity. Outputs from CSD [48] often exhibit characteristic yellowish hue and a less realistic, cartoon-lite -iie appearance, which TraCe avoids, producing more natural color rendition and photorealism. When compared against VSD [45], our model better interprets complex textural and stylistic prompts, accurately capturing the text's message and generating more coherent content. Contrasting with SDS [47], our results exhibit superior sharpness and finer details in both geometry and texture, leading to more visually appealing and realistic outputs. While ISM [23] can produce coherent structures, its outputs often exhibit stylized, painterly quality; in contrast, our TraCe generates

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results with enhanced photorealism and more natural material appearance. These results demonstrate our method's effectiveness in generating detailed and accurate 3D geometry and appearance from the given text descriptions.
Quantitative Comparison. We quantitatively evaluate our TraCe against other methods using 83 distinct prompts from Dreamfusion online gallery² with 120 views per prompt. We benchmark generation quality using CLIP Score (%), GPTEva13D (Overall) (which leverages GPT-4o for evaluation), and ImageReward. CLIPP Scores are evaluated with ViT-L/14, ViT-B/16, and ViT-B/32 backbones. We also assess computational efficiency via processing time (Time) and average peak VRAM (VRAM). As shown Table 1, the proposed TraCe achieves state-of-the-ar generation quality, securing top CLIP Scores across all ViT backbones, e.g., 69.2609 + 7. 7.8366% with ViT-L/14, Furthermore, TraCe demonstrates superior performance in advanced perception metrics, yielding the highest GPTEva13D score of 1028.03 and the most favorable (least negative) ImageReward score 00.2855 = 0.8909, indicating enhanced aesthetic quality and semantic alignment. With an average processing time of 14 minutes and average peak VRAM usage of 18741 MiB, TraCe offers high-fidelity generation with a compelling balance of qualitative performance, computational efficiency, and memory footprint.
Table 1: Quantitative comparisons. Comparison of different methods on CLIP Score, GPTEva13D Score, ImageReward Score, running time, and VRAM usage. We report mean and standard deviation across 83 prompts and 120 views.
CLIP Score (%)
GPTEval3D (Overall)
Method
RewarR
Time
VRAM
VIT-L/14
VIT-B/16
VIT-B/32
SDS [47]
68.6146- 4.9134
27.7049 +-7700
27.5561 +3,5893
1018.09
-0.4329+-..9125
10min
18147MiB
CSD
68.0282=7.5000
27,0886:133.734
26.58441138877
983.04
0.66155:0.74822
11min
19804MBB
VSD [45]
27.0749 +3.9675
26.9722 +-3 95663
1007.49
-0.5330+0.8827
17min
26473MiB
[23]
69.0093-+10.24000
27.5460-133.6 6817
26.9822.4:3.56 5,45
1012.37
-0,3904-:095003
20min
10151
SDI [29]
63.0409 11.7884
25.6487 H:5 .2540
25.5421 1:5.0
971.98
-0.8334 11.099
10min
16011
TraCe
69.2609
37.9334-33.733
27.7049
1028.03
-0,2855 10885
14min
18741MiB
CSD
Naive bridge
Ours LoRA Schedaled I-Sampling
Ours Scheduled Sampling
Ours
Figure Ablation study on our framework.
Ablation Study. Figure showcases the ablation study of our TraCe fox generation. VSD [45] and CSD [48] exhibit less-desired generation (e.g., missing details). The third column illustrates a naive Schrödinger Bridge approach [30] which attempts bridge distributions defined by source and target prompts and results in a comparatively smoother, less detailed rendering. The fourth column shows TraCe without LoRA adaptation and without our scheduled t-sampling, where noticeable artifacts such as blue hues on the fur are apparent. Introducing LoRA but omitting the scheduled t-sampling (fifth column) mitigates some artifacts, yet color inconsistencies persist. Finally, our full TraCe method ("Ours"") supported by LoRA- Aadapted learning of its specific score dynamics and an annealed t-sampling schedule generates significantly higher-fided fidelity details in the fur and tail, boosting overall realism compared to other methods (VSD, CSD) and ablated versions. These results highlight the role of our core Schrödinger Bridge formulation: it achieves superior final quality when augmented with these tailored learning components.

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We perform an ablation study on our key com- ponents, LoRA adaptation and scheduled sampling, measuring quality with ImageReward (Table 2). Our full method (-0.2486) significantly outperforms the baseline (both off: -0.4488), as well as enabling only LoRA (-0,4020) or only scheduled i-sampling (-0.3389). The results con-
Table 2: ImageReward ablation over LoRA and scheduled f-sampling.
Method Configuration
ImageReward (1)
LoRA off scheduled (-sampling off
-0.4488 0,9964
LoRA off & scheduled t-sumpling
-0.3389 0.9721
LoRA on & scheduled t-sampling off
-0.4020 + 1.0019
LoRA on & scheduled t-sampling on (ours)
-0.2486 + 0.8909
firm both components are crucial and demon-
strate their strong synergistic effect.
CFG value. We investigate the impact of the CFG value on our TraCe, illustrated in Figure 6 with two example objects. While very low CFG values (c.g.. 5) yield reduced visual fidelity, TraCe produces high-quality, well-defined results starting outcomes are stable and robust within the CFG 15-20 range. Beyond this, at higher CFG values (25-100), results remain largely consistent with minimal further improvement. This demonstrates TraCe's capability to effectively generate high-quality 3D assets at relatively low and stable CFG settings. Furthermore, TraCe's s enhanced visual quality complemented by its robust CLIP score performance within moderate CFG range (e.g., 10-30) relative to other compared methods, as detailed in Figure ??.
CFG of approximately 15-20. The visual
Figure 6: Different CFG value and generated 3D assets. Prompts are "an overstuffed pastrami sandwich" (top row), "a car made out of sushi" (bottom row).
6 Conclusion
We introduce Sepiecttry-Centrii Distillation (TraCe), a novel text-to-3D generation framework. Our approach is rooted in new theoretical understanding of SDS specific instance of the Schrödinger Bridge problem. The proposed TraCe explicitly constructs and learns a direct diffusion bridge between current renderings and text-conditioned targets, employing LoRA-adapted diffusion model to accurately model the bridge's score dynamics. Comprehensive experiments demonstrate TraCe's ofate-of-the-art performance, yielding 3D assets with superior visual quality and fidelity, notably at lower and more stable Classifier-Free Guidance values than prior methods. These results underscore the benefits of our principled, direct optimization trajectory. We believe TraCe will offer new insights for text-to-3D generation, in terms of efficient and robust trajectory learning for generative models.
7 Acknowledgments
This work was supported in part by the National Science Foundation of China under Grants (62472375), and in part by the Major Program of National Natural Science Foundation of Zhejiang (LDD24F020014, LD25F020002), and in part the Zhejiang Pioneer (Jianbing) (2024402000 and in part by the Ningbo Yongjiang Talent Programme(2023A-195 198--G..
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Answer: [Yes]
Justification: We establish novel theoretical connection, demonstrating that SDS can be precisely understood as a specific case of the Schrödinger Bridge framework. Experiments demonstrate that our TraCe achieves high-quality 3D generation, surpassing current state-of-the- art techniques. See the abstract and the end of Section 1.
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20


Reviews:
[{"review_id": "5fh0Made0q", "reviewer": "Reviewer_z2hB", "summary": "This paper introduces Trajectory-Centric Distillation (TraCe), a new optimization framework for text-to-3D generation. The authors establish a theoretical connection between Score Distillation Sampling (SDS) and Schrödinger Bridge (SB) problems, showing SDS as a special case. They then leverage this connection to construct a mathematically principled diffusion bridge between the current rendering and a text-aligned target image. Using this bridge, they train a LoRA-adapted diffusion model to guide 3D optimization, demonstrating superior performance, especially at lower CFG values, compared to existing state-of-the-art methods like SDS, VSD, and SDI.", "questions": "1. It's unclear how significant the adaptation via LoRA is. How much of the improvement is from using the SB trajectory versus simply adapting the diffusion model?\n\n2. The 2D experiments show blurry results. Could more analysis be added regarding this?", "limitations": "More description about the limitations should be added.", "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\n1. Establishing that SDS is a special case of the Schrödinger Bridge can provide theoretical insights to the community.\n\n2. Experiments (quantitative and qualitative) demonstrate that TraCe outperforms baseline methods in fidelity, detail, and texture quality, especially at low CFG values.\n\n3. The paper includes qualitative ablations to show the effectiveness of each component.\n\nWeaknesses:\n\n1. The paper heavily relies on CLIP scores, which may not fully capture geometry quality or 3D consistency. Adding metrics like FID on rendered views and 3D metrics would strengthen the claims. Consider moving the human study results from the supplementary to the main manuscript.\n\n2. A more comprehensive quantitative comparison with recent state-of-the-art 3D generation methods is needed.\n\n3. The diversity of the generated objects appears limited and could be further improved.", "was_revised": true, "final_justification": "The paper presents a solid analysis connecting Score Distillation Sampling (SDS) to the Schrödinger Bridge framework and introduces Trajectory-Centric Distillation (TraCe), an optimization method for text-to-3D generation. The contributions are well-motivated and demonstrate good performance. After reviewing the questions raised by other reviewers and the authors’ detailed rebuttal, I have decided to maintain my recommendation as a borderline accept.", "rebuttal": "> **[W1] Additional Evaluation Metrics**\n\nWe thank the reviewer for your insightful suggestions on strengthening our evaluation.\n\nWe chose the CLIP score for our quantitative analysis to ensure our results are fairly compared with prominent works in the field, such as ProlificDreamer, DreamFlow, and Score Distillation via Reparametrized DDIM, which **all use it as a key metric**. Moreover, to address the exact concerns about geometry and 3D consistency, we supplemented this with a user study involving 60 participants referring to DreamFlow’s user study settings. This study directly evaluated perceptual qualities that quantitative metrics cannot, including 3D consistency, photorealism, and prompt fidelity. The results, detailed in the supplementary (Tables 1-3), show a clear user preference for TraCe. While metrics like FID can assess rendered image realism, they don't capture 3D consistency or text alignment, and most 3D metrics require ground-truth data that is not available for text-to-3D generation. At the same time, human perceptual evaluation is often more persuasive than automated metrics [20]. We believe our user study provides a more holistic and meaningful assessment of quality for this task.\n\nIn response to reviewer’s suggestion, we have also conducted additional quantitative experiments (please refer to **the tables in Reviewer XMDr W2**). We selected two recognized and common evaluation metrics for the task of 3D asset generation: GPT-4o (with an implementation based on GPTEval3D) and ImageReward (with an implementation based on T³Bench). We would also like to respectfully refer the reviewer to the supplementary material, where extensive qualitative results (Figures 4, 7-12) further demonstrate the practical improvements in geometric detail and 3D coherence our method provides. We will follow your excellent suggestion to move the user study results into the main paper.\n\n> **[W2] Comparison with More SOTA Methods**\n\nWe thank the reviewer for the feedback. For the comparison, we selected the five most commonly used and state-of-the-art methods from SDS-based works. \n\nIn response to reviewer’s suggestion, we have now added new comparison methods: Consistent3D (2024) and DreamerXL (2024). **Please refer to the tables in Reviewer XMDr W2.** The new experiments evaluate TraCe using two state-of-the-art benchmarks: T³Bench, which is based on the ImageReward score, and GPTEval3D, which uses GPT-4o for a multi-faceted assessment. The results from both benchmarks demonstrate TraCe's superior performance. \nIn T³Bench evaluation, a higher score (closer to zero) is better. TraCe achieves the highest score of -0.2855, significantly outperforming all other methods, including the new comparison methods DreamerXL (-0.3382) and consistency (-0.5497). This is achieved with a competitive optimization time of 14 minutes.\n\nGPTEval3D provides a more detailed breakdown. TraCe achieves the highest score across all six categories evaluated by GPT-4o: 3D Plausibility, Texture Details, Geometry Details, Text-Asset Alignment, Text-Geometry Alignment, and Overall. Notably, in the \"Overall\" assessment, TraCe scores 1028.033, showing a clear lead over other methods.\n\n> **[W3] Regarding Generation Diversity**\n\nUnlike other SDS-based methods, our method's diversity is not negatively impacted because we use a low CFG value.\n\nWe agree this is an important aspect, and it is often linked to a trade-off with generation quality via the CFG value. It is well-known that high CFG values can reduce diversity by forcing the model into a narrow mode of the distribution. A key advantage of our method (TraCe) is its ability to achieve high-fidelity results at low and stable CFG settings (e.g., 15-20), which is better for preserving the natural diversity offered by the diffusion prior. While we do not claim that TraCe fundamentally solves the diversity challenge for SDS-based methods, its operational characteristics are more conducive to preserving variety compared to methods that rely on high CFG for quality.\n\nOur experiments in the supplementary material (Section H, Figure 5) demonstrate this capability. For prompts like \"an amigurumi motorcycle\" or \"an overstuffed pastrami sandwich,\" TraCe produces multiple distinct 3D instances with clear variations in geometry, structure, and style. While we present this to show that our method generates varied and plausible assets , we also note that this level of diversity is in line with that of other leading score distillation methods.\n\n> **[Q1] Ablation Study on LoRA Adaptation**\n\nWe thank the reviewer for this insightful question regarding the significance of the LoRA adaptation versus the Schrödinger Bridge (SB) trajectory. To precisely disentangle these effects, we have conducted a new quantitative ablation study, complementing the qualitative results in Figure 5. We evaluated different configurations of our method using ImageReward, and we used 43 prompts from DreamFusion online gallery [1] for generation.\n\nThe results clearly show that both components contribute significantly and, more importantly, work synergistically to achieve the best performance (we keep other hyper-parameters the same for fair comparisons):\n\n| Method Configuration                      | ImageReward Score ($ \\uparrow $) |\n| ----------------------------------------- | --------------------- |\n| LoRA off & scheduled t-sampling off       | -0.4488 $\\pm$ 0.9964       |\n| LoRA off & scheduled t-sampling on        | -0.3389 $\\pm$ 0.9721       |\n| LoRA on & scheduled t-sampling off        | -0.4020 $\\pm$ 1.0019       |\n| LoRA on & scheduled t-sampling on (TraCe) | -0.2486 $\\pm$ 0.8909       |\n\nEnabling the scheduled t-sampling alone provides a strong foundation, significantly improving the score from -0.4488 to -0.3389. This highlights the inherent benefit of optimizing along the more stable trajectory from source to target defined by our SB formulation. Similarly, adding LoRA adaptation in isolation also improves the baseline score, demonstrating that allowing the diffusion model to adapt is beneficial. Moreover, the full TraCe method, which combines both components, achieves the best score of -0.2486. This result is substantially better than applying either component individually, demonstrating a clear synergistic effect. This shows that the LoRA-adapted model performs best when it is trained to learn the specific score dynamics of the SB trajectory from source to target.\n\n[1] https://dreamfusion3d.github.io/gallery.html\n\n> **[Q2] Analysis of Blurry Results in 2D Experiments**\n\nThank you. \n\nThe 2D experiment presented in the supplementary material (Section F, Figure 3) is designed as a diagnostic tool to isolate and directly compare the behavior of different score distillation gradients, removing the complexities of 3D representations. This type of analysis, where a 2D image is optimized directly, has been used in prior work (e.g., VSD) to understand the inherent properties of the guidance signal itself.\n\n**The goal of this experiment is not to compete with state-of-the-art, multi-step 2D text-to-image samplers, but rather to demonstrate the *relative* improvement of the TraCe gradient** over other score distillation losses like SDS, CSD, and VSD. As shown in Figure 4 in main manuscript and Figures 4, 7-12 in the supplementary, our method consistently generates images with **enhanced visual fidelity, quality, and fewer artifacts compared to these other distillation techniques.** For example, the results from SDS often contain noise, CSD can produce overly stylized outputs, and VSD can lack sharpness. Our method mitigates these issues, yielding more realistic textures and clearer details.\n\nThis analysis provides evidence that our TraCe framework offers a fundamentally more stable and accurate guidance signal. This improvement in the 2D domain directly translates to the superior quality and reduced artifacts we observe in the more complex task of text-to-3D generation."}, {"review_id": "K7CGjA2q4U", "reviewer": "Reviewer_XMDr", "summary": "This paper tackles the problem of artifacts such as over-saturation and over-smoothing in SDS optimization-based text-to-3D generation methods by theoretically connecting SDS to the Schrödinger Bridge framework and showing that SDS is a simplified instance of this optimal transport approach. The authors introduce Trajectory-Centric Distillation (TraCe), which explicitly constructs a diffusion bridge between current renderings and their text-conditioned targets, training a LoRA-adapted model on the trajectory's score dynamics to enable high-quality generation with smaller Classifier-free Guidance values.", "questions": "Please see the weaknesses section.", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n- The paper is well-written, highly organized and easy to follow.\n- The contribution of the paper in interpreting SDS in the perspective of Schrödinger Bridge is novel, robust and significant, providing meaningful contribution to the field of score distillation based 2D / 3D generation. Theoretical explanation and proof of this interpretation, provided in the paper is robust and sound.\n- The authors translate this interpretation to the methodology well, using the rendered image $x_{rndr}$ and one-step denoised image $x_{0}^{pred}$ as two endpoints of the Schrödinger Bridge and formulating the optimization process as interpolation of two diffusion denoising paths. \n\n**Weaknesses:**\n- The improvement from this method, shown in the experimental section of the paper, seems to be somewhat marginal, unable to achieve meaningful modification in overall geometry but only in texture. Can the authors provide examples in which i) baseline result produces divergent 3D scene (such as Janus problem) but TraCe results in significant improvements from it, or ii) results in which generated result's geometry and layout differs significantly due to usage of TraCe? This seems to be my main concern with the paper, and if this point is elaborated (regarding specifically *how* TraCe improves upon SDS process in implementation), I would raise my score toward acceptance.\n- Both quantitative and qualitative results seem to be lacking in the main paper: can additional experiments (especially qualitative) be provided to back up that TraCe is effective in practice and not only in theory?\n- The paper is unclear in how the LoRA-adapted model $\\epsilon_\\phi(x_t, t, y, c)$ is trained to predict the noise from $x_t$ to $x_{0}^{pred}$: please elaborate. Is it trained online during optimization like LoRA-adapted model in ProlificDreamer (that does seem to be likely)? If this is the case, can this method be seen as a variant of VSD under single-particle setting?", "was_revised": true, "final_justification": "After careful consideration of the rebuttal and discussions, I raise my recommendation toward acceptance based on the following assessment:\n\n- The theoretical contribution interpreting SDS through the Schrödinger Bridge perspective is novel, robust, and significant, providing meaningful advancement to score distillation-based 2D/3D generation.\n- The mathematical framework and proofs supporting this interpretation are sound and well-established.\n- The authors successfully translate this theoretical insight into a practical methodology, effectively using rendered image and one-step denoised image as Schrödinger Bridge endpoints.\n- During the rebuttal phase, the authors have provided extensive results to convince me of their method's effectiveness, even though shortcomings remain. Still, I see this paper has meaningful contributions to the field which can be expanded upon by later work.", "rebuttal": "> **[W1] Addressing Geometric Improvements and the Janus Problem**\n\nThanks for the comment. The reviewer’s main concern is understanding *how* our TraCe improves upon the SDS process to justify its results, particularly concerning geometry.\n\n**The primary goal of TraCe is not to solve fundamental 3D-awareness issues like the Janus problem or to generate entirely different scene layouts from baselines.** Instead, TraCe targets a different, but equally critical, challenge in text-to-3D generation: **the quality and the fidelity of the optimized 3D asset**. Like other works [20] [23] [29] [30] [45] [48] that aim to refine the distillation process, our focus is on improving the quality and fidelity of the final result by addressing instabilities and artifacts inherent in the standard SDS framework.\n\nThe proposed TraCe makes significant and consistent refinements to geometric quality and coherence. Our qualitative results provide several examples of this:\n1. TraCe is highly effective at removing geometric artifacts. For instance, in \"a candelabra with many candles on a red velvet tablecloth\" (Figure 7 in supplementary), it replaces the outrageous flame geometry from GaussianDreamer with controlled, plausible flames. \n2. TraCe generates finer structural details. When generating \"A gothic cathedral with stained glass windows and tall arches\" (Figure 8 in supplementary), the cross atop the main spire has a clear and reasonable geometry, a detail that is misshapen in the ProlificDreamer output.\n3. For the \"blue lobster\" and \"a ladybug\" (Figure 7 in supplementary), our method eliminates the extraneous geometry seen in the baseline, such as the lobster's massive, disjointed green antennae and the ladybug's misshapen feet.\n4. In \"a mug of hot chocolate with whipped cream and marshmallows\" (Figure 10 in supplementary), the distracting \"cloud\" of color from Classifier Score Distillation is gone, resulting in a more coherent shape.\n\n---\n\nRegarding the Janus (multi-face) problem, we agree this is a crucial challenge. However, this is a known limitation stemming from the underlying 2D text-to-image prior, which inherently lack 3D awareness. Therefore, like other SDS-based methods [20] [23] [29] [30] [45] [48], etc., TraCe is not designed to be a fundamental solution to this issue. We use standard mitigation techniques like negative prompting to mitigate the Janus problem. One way to address Janus problem is to use 3D-aware multi-view diffusion model (e.g., MVDream), and our framework is compatible with such models for 3D optimization. This will be discussed in revised version.\n\n> **[W2] Additional Qualitative and Quantitative Results**\n\nWe thank the reviewer for their valuable feedback on the presentation of our results.\n\n---\n\nFor our quantitative evaluation, we used the **CLIP score** and **a detailed user study**. This multi-faceted approach was chosen deliberately. The CLIP score aligns our work with the evaluation practices of prominent text-to-3D papers like ProlificDreamer [45], DreamFlow [20], and Score Distillation via Reparametrized DDIM [29]. At the same time, human perceptual evaluation is often more persuasive than automated metrics [20]. Therefore, following the example of methods like DreamFlow, we conducted a rigorous user study with 60 participants referring to DreamFlow’s user study settings, which shows a consistent preference for TraCe in 3D consistency, prompt fidelity, and photorealism.\n\nIn response to reviewer’s suggestion, we conduct additional quantitative experiments, the results of which are available in the tables below. We selected two community-recognized and common evaluation metrics for the task of 3D asset generation: GPT-4o (with an implementation based on GPTEval3D) and ImageReward (with an implementation based on T³Bench). The combination of the user study, CLIP scores, and the extensive qualitative results in the supplementary material provides strong practical backing for the theoretical advancements presented in our work. \n\n---\n\nRegarding the qualitative results, we presented key comparisons in the main paper due to page limitations, with the full, extensive evidence contained in the supplementary material. We respectfully refer the reviewer to the supplementary document, which provides a comprehensive demonstration of TraCe's practical effectiveness across numerous examples and against six state-of-the-art methods (Figure 4 in main manuscript and Figures 7-12 in supplementary). The supplementary also includes detailed gradient visualizations (Figure 4 in supplementary) , an ablation study of the CFG value (Figure 1 in supplementary)). We will provide more in supplementary in revision. \n\n| Method                        | GPT-4o (GPTEval3D) - 3D Plausibility | GPT-4o (GPTEval3D) - Texture Details | GPT-4o (GPTEval3D) - Geometry Details | GPT-4o (GPTEval3D) - Text-Asset Alignment | GPT-4o (GPTEval3D) - Text-Geometry Alignment | GPT-4o (GPTEval3D) - Overall |\n| ----------------------------- | ------------------------------------ | ------------------------------------ | ------------------------------------- | ----------------------------------------- | -------------------------------------------- | ---------------------------- |\n| **sds** (11min)               | 953.43                              | 1022.40                             | 1003.04                              | 1038.08                                  | 1023.93                                     | 1018.09                     |\n| **vsd** (17min)               | 1020.81                             | 985.59                              | 996.29                               | 993.04                                   | 1006.36                                     | 1007.49                     |\n| **csd** (11min)               | 1009.29                             | 953.43                              | 984.24                               | 1024.24                                  | 950.82                                      | 983.04                      |\n| **sdi** (10min)               | 1002.51                             | 949.00                              | 970.09                               | 981.04                                   | 973.58                                      | 971.98                      |\n| **ism** (20min)               | 1003.79                             | 951.63                              | 998.94                               | 1007.07                                  | 989.78                                      | 1012.37                     |\n| **consistency** (new, 14 min) | 981.48                              | 1001.88                             | 1013.99                              | 986.38                                   | 995.42                                      | 993.79                      |\n| **DreamerXL** (new, ~1h)        | 1005.58                             | 997.22                              | 1002.94                              | 1032.20                                  | 1012.37                                      | 1014.49                     |\n| **TraCe** (ours, 14min)       | 1025.42                             | 1031.98                             | 1014.03                              | 1032.41                                  | 1024.45                                     | 1028.03                     |\n\n| **Method**               | **ImageReward (T³Bench) $ \\uparrow $** |\n| ------------------------ | ---------------------------- |\n| SDS (11min)              | -0.4329 $ \\pm $ 0.9125              |\n| vsd (17min)              | -0.5330 $ \\pm $ 0.8927              |\n| csd (11min)              | -0.6715 $ \\pm $ 0.7482              |\n| sdi (10min)              | -0.8334 $ \\pm $ 1.0391              |\n| ism (20min)              | -0.3904 $ \\pm $ 0.9503              |\n| consistency (new, 14min) | -0.5497 $ \\pm $ 0.9200            |\n| DreamerXL (new, ~1h)       | -0.3382 $ \\pm $ 0.9225           |\n| TraCe (ours, 14min)      | -0.2855 $ \\pm $ 0.8909           |\n\n> **[W3] Methodological Details and Comparison to VSD**\n\nWe thank the reviewer for this insightful question and the opportunity to clarify our method. You are correct that the LoRA-adapted model is trained online, concurrently with the 3D model. However, the underlying principle of our TraCe framework is fundamentally different from that of Variational Score Distillation (VSD).\n\nThe key differences are as follows: \n\nIn VSD, the LoRA-adapted model is trained to approximate the score of the entire distribution of current (source) renderings, which is also mentioned in [30]. Its goal is to perform variational inference by matching two distributions.\n\nIn contrast, **our TraCe framework does not model the distribution of currrent** **renderings**. This is where the novelty of TraCe's LoRA training lies. Instead of learning a distributional score like VSD, our LoRA model $\\epsilon_{\\phi}$ is trained via a distinct objective: **learning the transition of the point x_t on the bridge trajectory between the current rendering $x_{rndr}$ and the ideal target $x_0^{pred}$.** This provides direct supervision for the score function along this specific trajectory. This online adaptation is essential, as a pre-trained T2I model has no knowledge of the dynamics of our constructed Schrödinger Bridge between two arbitrary distributions. We are not merely specializing the model, but rather training it on a fundamentally different and more direct learning signal than the distributional objective used in VSD.\n\nAlso, we appreciate the reviewer pointing out this potential ambiguity and will revise Section 4.2 in revision to make this critical distinction more explicit."}, {"review_id": "Vn7HhOAId6", "reviewer": "Reviewer_iYfs", "summary": "Summary:\n\nThe paper theoretically establishes Score Distillation Sampling (SDS) as a simplified instance of the Schrödinger Bridge and introduces the TraCe framework, which enables more stable 3D optimization. Experiments demonstrate that TraCe outperforms existing methods in terms of visual quality and text alignment.", "questions": "1、Please clarify the novelty of the proposed work.\n\n2、Please clarify the differences between this work and prior works with similar ideas, such as DreamFlow [2] and I²SB [1].\n\n3、Why the generated results still have artifacts such as over-saturation and over-smoothing?\n\n[1] Liu, Guan-Horng, et al. \"I $^ 2$ SB: Image-to-Image Schr\\\" odinger Bridge.\" arXiv preprint arXiv:2302.05872 (2023).\n\n[2]Lee, Kyungmin, Kihyuk Sohn, and Jinwoo Shin. \"Dreamflow: High-quality text-to-3d generation by approximating probability flow.\" arXiv preprint arXiv:2403.14966 (2024).", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\nThis paper presents quantitative and qualitative comparisons with other methods.\n\nWeaknesses：\n\n1、A related work has proved that Score-based Generative Model (SGM) is a special case of Schrödinger Bridge [1]. \n\n2、This work adopts the tractable Schrödinger Bridge (SB) framework introduced in related work. \n\n3、The results of the proposed method have still artifacts such as over-saturation and over-smoothing.\n\n4、The paper lacks a comparison with Dreamflow[2].\n\n5、There are formatting issues in the references, e.g., Reference 26.\n\n[1] Liu, Guan-Horng, et al. \"I $^ 2$ SB: Image-to-Image Schr\\\" odinger Bridge.\" arXiv preprint arXiv:2302.05872 (2023).\n\n[2]Lee, Kyungmin, Kihyuk Sohn, and Jinwoo Shin. \"Dreamflow: High-quality text-to-3d generation by approximating probability flow.\" arXiv preprint arXiv:2403.14966 (2024).", "was_revised": true, "final_justification": "I have considered rebuttal and discussions with authors, other reviewers and AC. I raise my score to 4 (borderline accept).", "rebuttal": "We thank the reviewer for your time and feedback. However, we believe there have been several fundamental misunderstandings regarding our paper's novelty, contributions, and results. We would like to take this opportunity to clarify these points.\n\n> **1. On the Novelty of Our Work (Q1 & Q2; W1, W2, W4)**\n\nThe reviewer’s primary concerns appear to stem from a misunderstanding of our work's core novelty. \n\n**Our Theoretical Contribution (vs. W1):** We would like to clarify a key distinction. Our paper does **not** claim that \"SGM is a special case of Schrödinger Bridge\" is a novel finding. We state this as established background in our preliminaries (Section 3). Our novel theoretical contribution, as stated in the introduction and proven in Section 4.1, is to be the **first to formally establish that Score Distillation Sampling (SDS) is a simplified instance of the Schrödinger Bridge framework**. This insight allows us to formulate TraCe to learn a direct, optimal transport trajectory to the target, which enables the generation of higher quality and fidelity assets with lower and more stable CFG values.\n\n**Our Methodological Contribution (vs. W2 & I2SB [26]):**  Building upon the Schrödinger Bridge (SB) framework is standard practice in community, such as [A] [B] [C]. **Our novelty lies in how to better solve the problem of score distillation for text-to-3D generation with the use of this framework.** Our TraCe introduces a new formulation where we construct a diffusion bridge specifically from the current 3D render ($x_{rndr}$) to its dynamically estimated denoised target ($x_0^{pred}$). We then train a LoRA-adapted model to learn the score dynamics of this specific trajectory. This unique formulation is the core of TraCe and is not presented in I2SB [26] or other prior works. \n\n**Comparison with DreamFlow [20] (vs. W4):** We explicitly discussed DreamFlow and differentiate our work in Section 2 (Related Work) of the submission. As we note, DreamFlow \"proposes to approximate the backward Schrödinger Bridge dynamics between rendered and target views by simply repurposing a fine-tuned text-to-image model, a heuristic potentially deviating from the true underlying Schrödinger Bridge process\". It is **a heuristic approach that approximates the Schrödinger Bridge dynamics, unfortunately without the theoretical analysis that underpins our work**. In contrast, TraCe is more principled: we explicitly construct the Schrödinger Bridge and train a model on its true score dynamics grounded in the analytical formulation, leading to a more stable and direct optimization trajectory.\n\n> **2. On the Quality of Generated Results (Q3; W3)**\n\nWe are sorry some misunderstanding is caused to you. In fact, a primary motivation and demonstrated contribution of our work is the **significant reduction** of these very artifacts compared to prior works. \n\n**Superior Fidelity:** Throughout the qualitative comparisons in Figure 4, our method consistently produces sharper details and more naturalistic textures (e.g., the fur on the \"fox,\" the details of the \"wedding cake\", the texture of “golden globe”) compared to strong baselines including VSD, SDS, CSD, ISM, etc.\n\n**Direct Visual Evidence:** In Figure 1, the results from standard SDS and VSD show clear artifacts (e.g., over-saturation, blurriness), while our result is visibly cleaner and more detailed at a fair CFG value.\n\n**Qualitative and Quantitative Results:** This visual superiority is backed by our state-of-the-art quantitative CLIP scores reported in Table 1: Quantitative comparisons. We provide qualitative comparisons in the main paper (Figures 4) and supplementary materials (Figures 4, 7-12) that visually demonstrate our method's superiority. More importantly, we conducted a comprehensive user study with 60 participants (Supplementary Section D) showing a clear user preference for TraCe, and we believe human perceptual evaluation is often more persuasive than automated metrics [20]. We also provide additional quantitative experiments, and please refer to the **tables in Reviewer XMDr W2**. \n\n> **3. Minor Formatting Issues (W5)**\n\nThank you! We have corrected such issues and will ensure the paper will be thoroughly proofread in the revised version.\n\n---\n\nWe hope these clarifications address your concerns, and effectively communicate the novelty of our theoretical insights, our proposed TraCe framework, and the significance of our experimental results. Thank you again.\n\n---\n\n[A] Xuan Su, Jiaming Song, Chenlin Meng, and Stefano Ermon.\nDual diffusion implicit bridges for image-to-image translation. In International Conference on Learning Representations, 2023.\n\n[B] Yuyang Shi, Valentin De Bortoli, Andrew Campbell, and Arnaud Doucet. Diffusion schrödinger bridge matching. Neural Information Processing Systems (NeurIPS), 2023.\n\n[C] S. Diefenbacher, G.-H. Liu, V. Mikuni, B. Nachman, and W. Nie, Improving generative model-based unfolding with Schrödinger bridges, Phys. Rev. D 109 (2024), no. 7 076011, [arXiv:2308.12351]."}, {"review_id": "ZSTM3jIHV4", "reviewer": "Reviewer_ifTq", "summary": "This paper introduces Trajectory-Centric Distillation (TraCe), a new framework for text-to-3D generation that reformulates the Score Distillation Sampling (SDS) approach under the Schrödinger Bridge framework. By utilizing LoRA adaptation and an annealed sampling schedule, TraCe mitigates over-saturation and over-smoothing artifacts that often occur with high classifier-free guidance (CFG) values in existing methods.", "questions": "1. The experimental setup raises concerns. In Table 1, the reported optimization time for VSD is questionable. In NeRF-based representations, VSD typically requires at least 2.5 hours per object, and even with Gaussian representations, it is unlikely for the training time to be shorter than that of ISM. Moreover, the default optimization steps for related methods are generally around 5000, whereas this work only uses 1700 steps, which may artificially reduce the reported optimization time. Even though incorporating LoRA may significantly increase training time, it is important to ensure that each model is fully converged before making fair comparisons.\n\n2. The chosen evaluation metric (CLIP Score) does not align well with the stated motivation of improving texture quality and overall visual fidelity. CLIP primarily measures text-image alignment and cannot sufficiently evaluate texture quality. To support the claims more robustly, it would be more appropriate to incorporate human-aligned evaluation protocols, following GPT-4V(ision) or T^3Bench.\n\n3. The paper lacks comparisons with some closely related and recent works, such as:\nConsistent3D: Towards Consistent High-Fidelity Text-to-3D Generation with Deterministic Sampling Prior\nDreamer XL: Towards High-Resolution Text-to-3D Generation via Trajectory Score Matching\n\n4. The ablation study lacks quantitative evaluation, making it difficult to rigorously assess the contribution of each component. Additionally, the distinction between the naive bridge and the proposed TraCe remains unclear. From my understanding, both approaches appear to rely on Equation (4) to update the 3D representation. Furthermore, the role of LoRA seems limited to color correction, yet incorporating LoRA significantly increases optimization time. This raises questions about whether the additional complexity and computational cost introduced by LoRA are justified by corresponding performance gains.", "limitations": "This work lacks a discussion about limitations and failure cases.\n- Please analyse failure cases.\n- Sensitivity to LoRA fine-tuning stability and the risk of underfitting or mode collapse.", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "# Strengths\n- The paper provides a theoretical analysis connecting SDS to Schrödinger Bridge, which offers a fresh perspective on optimization-based 3D generation.\n- Mathematical descriptions, especially of the bridge construction and gradient computation, are clearly presented and well supported by visual diagrams.\n\n# Weaknesses\n- Although the paper claims that the proposed Trajectory-Centric Distillation effectively mitigates over-saturation and over-smoothing artifacts, the qualitative results do not convincingly demonstrate a clear superiority in visual quality. Specifically, it is unclear why Figure 4 does not use exactly the same text prompts and view settings as related works for direct comparison. In both Figure 4 and the Appendix, the results produced by Trajectory-Centric Distillation still exhibit noticeable smoothness and blurriness.\n\n- The experimental setup appears questionable. While the main focus of the method is to improve text fidelity, the quantitative evaluation primarily relies on CLIP Score, which mainly reflects text-image alignment and does not adequately assess texture or geometric fidelity. Moreover, the visual results seem weaker than those in prior works, and the implementation details provided are insufficient, raising concerns about the fairness and reproducibility of the experiments.\n\n- All experiments are conducted exclusively on Gaussian representations, and it remains unclear whether the proposed TraCe framework can outperform VSD when using NeRF representations.", "was_revised": true, "final_justification": "After the discussion, the major concern about the fairness of the comparison has been resolved. Although this work shows weaker visualizations, it provides better quantitative results. For this reason, I have raised the score.", "rebuttal": "> **[W1] Qualitative Evaluation and Comparison**\n\n**On the Fairness of the Qualitative Comparisons:** \n\nThe official code for some baseline methods we compare against—VSD, SDI, and CSD—are all implemented based on NeRF. To ensure a fair comparison, we utilized the 3DGS implementation within the Threestudio framework. Our parameter settings for the camera/pose are based on the settings for the 3DGS-based implementations from Threestudio. This is why our results may appear to differ from the NeRF-based view settings presented in their original papers. \n\nFurthermore, The text prompts used in our paper were sourced from the public DreamFusion online gallery [A]. These are standard, widely-used prompts that serve as a common benchmark in the community [20] [23] [29] [30] [35] [45] [48], ensuring our evaluation is relevant and consistent with established practices.\n\n---\n\n**On Smoothness and Blurriness in Results:** \n\nThe critique of smoothness often arises from comparisons to a specific family of methods, such as LucidDreamer (ISM) and Score Distillation via Inversion (SDI). These works aim to address over-smoothing by replacing the *stochastic random noising* of vanilla SDS with a deterministic term derived from **DDIM inversion**. This ensures the guidance is highly consistent, which is very effective for preserving sharp details. Our work, TraCe, introduces a novel and **orthogonal contribution**. We do not modify the stochastic noising process but instead provide **a more principled formulation for the new optimization objective** as a general version of SDS framework. **Therefore, these two categories of approaches are not mutually exclusive but are in fact complementary**. A very promising direction for future work is to combine our principled TraCe objective with a deterministic noising process from DDIM inversion. \n\n**Although TraCe was not designed to incorporate DDIM inversion specifically to solve the over-smoothing problem, it still effectively mitigates blurriness compared to prior methods.** For example, the intricate decorations on the cake (Figure 1), the sharp and defined patterns on the \"hermit crab with a colorful shell\" (Figure 4).\n\n---\n\n[A] https://dreamfusion3d.github.io/gallery.html\n\n> **[W2] Experimental Rigor and Reproducibility**\n\nRegarding \nthe explanation to experimental setup and more quantitative experiments, **please refer to the answer to Reviewer z2hB W1**.\n\nRegarding reproducibility, we have actually **provided the complete code for our project in supplementary materials** to ensure the reproducibility of our experiments.\n\n> **[W3] Generalization to NeRF**\n\nWe use the official implementation of VSD. We keep other hyer-parameters the same for fair comparisons. We use prompts from DreamFusion gallery. TraCe outperforms VSD in both evaluation metrics.\n\n| **Method**              | **GPT-4o (GPTEval3D)-3D Plausibility** | **GPT-4o (GPTEval3D)-Texture Details** | **GPT-4o (GPTEval3D)-Geometry Details** | **GPT-4o (GPTEval3D)-Text-Asset Alignment** | **GPT-4o (GPTEval3D)-Text-Geometry Alignment** | **GPT-4o (GPTEval3D)-Overall** |\n| ----------------------- | -------------------------------------- | -------------------------------------- | --------------------------------------- | ------------------------------------------- | ---------------------------------------------- | ------------------------------ |\n| VSD (~5h)               | 1261.80                                | 1058.73                                | 1152.00                                 | 1246.37                                     | 1180.56                                        | 1012.50                        |\n| **TraCe (ours, ~3.5h)** | 1289.89                                | 1127.06                                | 1228.94                                 | 1284.60                                     | 1245.06                                        | 1179.86                        |\n\n| **Method**              | **ImageReward (T³Bench) $ \\uparrow $** |\n| ----------------------- | ---------------------------- |\n| VSD (~5h)               | -0.6737 $\\pm$ 0.4098            |\n| **TraCe (ours, ~3.5h)** | -0.4533 $\\pm$ 0.4635            |\n\n> **[Q1] Fairness of Efficiency Comparison**\n\nThank you for your comment.\n\n---\n\nRegarding the optimization time for VSD, “the optimization time for ISM should be smaller than VSD” may be a misunderstanding. For ISM, we used its official 3DGS implementation with 5000 steps, which took approximately 20 minutes. For VSD, since our work uses a 3DGS representation, we experimentally determined its optimal settings for this different backbone. We found that performance peaked at around 2200 optimization steps. Training with fewer steps produced blurry assets, while training for longer introduced significant artifacts (e.g., large bright spots and widespread noisy colors), leading to degraded quality. We suspect this indicates that the VSD objective is less robust for 3DGS optimization. These 2200 steps yielded the best possible results for VSD in our setup and corresponded to the approximately 17-minute runtime reported in Table 1's quantitative comparisons in main paper. \n\n---\n\nRegarding the optimization steps for our method, we note that while older methods required ~5000 steps, the number of training steps for recent 3DGS-based methods is considerably lower, typically ranging from 1200 (e.g., GaussianDreamer) to 2500 (e.g., DreamerXL) steps. Our choice of 1700 steps for TraCe was similarly determined by empirical convergence. Our experiments showed that generated assets were fully converged at this point, with no significant quality improvement in further steps. Therefore, this number was not chosen to artificially shorten the time but represents the point of optimal quality for our method.\n\n---\n\nFinally, concerning the overhead of LoRA, our experiments show it adds only 1-2 minutes to the total generation time within our 3DGS framework. The significant quality improvements from TraCe are thus achieved with minimal additional computational cost.\n\n> **[Q2] Appropriateness of Evaluation Metrics**\n\nPlease see our response to W2.\n\n> **[Q3] Comparison with Recent Works**\n\nThank you for reviewer's suggestion. For our comparisons, we selected the five most commonly used and state-of-the-art methods from SDS-based works. \n\nIn response to reviewer’s suggestion, we have now added new comparison experiments with two latest works. For details, please refer to the **tables in Reviewer XMDr W2**.\n\n> **[Q4] Ablation Study, Method Comparison and LoRA Analysis**\n\nThank you for your suggestions. Regarding the ablation study, we have taken your feedback and conducted a new quantitative evaluation, which is detailed in the **table in Reviewer z2hB Q1**, and will be incorporated into the final version of the paper. We chose ImageReward, a community-recognized, SOTA evaluation method, as our evaluation metric.\n\n---\n\n**In response to your question about the distinction between TraCe and the \"Naive Bridge\"**, the two approaches are fundamentally different. The Naive Bridge proposed in [30] does not rely on Equation (4). It constructs a bridge between distributions defined by two separate text prompts (i.e., a source prompt and a target prompt). Its guidance is based on the difference between the model's predicted scores conditioned on source prompt (e.g., negative prompts such as \"oversaturated, smooth, pixelated...\") and target prompt (the base prompt). This method steers the optimization by manipulating the text conditioning of a standard diffusion model to naively approximate a bridge. \n\nTraCe constructs its bridge between two images: the current rendering ($x_{rndr}$) and a dynamically estimated ideal target ($x_0^{pred}$). Our goal is to learn the score function of this specific image-to-image trajectory. Therefore, the guidance term in our Equation (4), subtracts the **analytically-defined ground-truth noise** that connects an intermediate point on the bridge ($x_t$) to the bridge's endpoint ($x_{rndr}$), which helps learn to accurately follow a direct transport trajectory between two distributions.\n\nMoreover, the Naive Bridge approach is not a standalone method and requires an initial training stage using standard SDS to be effective. TraCe, in contrast, is a complete, end-to-end framework that operates effectively from the start of optimization. \n\n---\n\n**Regarding your questions about LoRA:**\n\nThe assertion that LoRA \"significantly increases optimization time\" is actually not the case in our framework. Our experiments show that incorporating LoRA adds **only 1-2 minutes** to the total generation time per asset.\n\nThis minimal cost is well-justified by the performance gains, as LoRA is crucial for addressing a key distributional mismatch. A standard diffusion model was not trained to predict the score for a Schrödinger Bridge between two arbitrary distributions (our current rendering and our ideal target). Applying it directly to this new task leads to prediction errors, which manifest as the artifacts you noted (e.g., incorrect colors, blurriness). Therefore, TraCe uses LoRA to specialize the diffusion model for this exact task. By training the LoRA parameters on samples along the bridge, we explicitly teach the model the score dynamics of this optimal, direct trajectory. \n\nAdditionally, the role of LoRA is not just limited to color correction. Our experiments show that LoRA also improves the details and sharpness of the generated assets and eliminates the formation of bright spots. Examples include the texture of animal fur, the details and clarity of flowers, and the intricacy of patterns on an axe, among others. Our new quantitative ablation **in table in Reviewer z2hB Q1** confirms this, showing that adding LoRA yields a more significant performance improvement than only adding scheduled t-sampling (ImageReward score from -0.3389 to -0.2486). This demonstrates its role is critical, not peripheral."}]

Author rebuttal:

Meta-review: The authors propose a new “generative” approach to transferring “text to 3D”. Their contribution is two-fold and proceeds with establishing an equivalence between the “text-to -3D” generation and the Schrodinger bridge in stochastic diffusion, followed with an extensive experimental validation, including numerous experiments requested (at times quite late) by reviewers. The question and rebuttal period has been, by many measures, thorough and informative given some of the reviewers’ pertinent comments and the prompt and equally conscientious responses by the authors.  
Specifically, they formulate the data generation process as that of learning an optimal transport problem between a source and a sought target distribution, thereby enabling high-quality generation and independence of Classifier-free Guidance (CFG) values. The authors first establish an SDS as a simplified instance of the Schrödinger Bridge framework, so that it effectively exploits the reverse process of a Schrödinger Bridge, which, under specific conditions (e.g., a Gaussian noise as one end), collapses to SDS's score function of the pre-trained diffusion model. A Trajectory-Centric Distillation (TraCe) is subsequently introduced as text-to-3D generation approach. 
 This paper had a long, extended and quite thorough exchange between the authors and the reviewers. The reviewers all agreed that the paper was theoretically solid and varied on the degree to which they thought the experiments validated the claims. Three of the reviewers who had an initially lower ranking, raised it upon their admission that the authors had been very vigilant, cooperative in punctually in answering all questions as well as running some requested experiments in a rather surprisingly timely fashion. All reviewers agreed that the contribution was theoretically solid but would have benefitted from additional experiments some of which had been run as a response.  They capped their scores borderline accept, still insisting more extensive experiments in addition to the included ablation studies and all other additional experiments run during the question-answer period. 
As an AC and having followed the back-and-forth discussion, believe that the paper has a contribution of merit, and that the authors have navigated the conceptual questions and admirably quickly have answered questions and delivered on the additional experiments they were requested to produce.  In light of this exchange, and of  the AC's sollicitation of a discussion  to potentially provide any strong leaning ,    and of the AC's own quick reading of the paper, the AC supports the acceptance of this paper.
Decision: Accept (poster)