SEGS: Structural Energy-Guided Sampling

• Structural Energy-Guided Sampling (SEGS) is a framework that uses a PCA-based structural energy from U-Net features to guide diffusion trajectories.
• It operates at sampling time without retraining, effectively mitigating the Janus problem by enforcing view-consistency in text-to-3D generation.
• The method’s principle extends to applications like molecular conformer generation and traffic prediction by biasing sampling with structural energy cues.

Searching arXiv for papers on Structural Energy-Guided Sampling and related energy-guided sampling methods. Structural Energy-Guided Sampling (SEGS) is a sampling-time framework in diffusion-based generative modeling that uses an explicitly defined structural energy and its gradient to steer generation trajectories toward structurally preferred states. In the usage most directly associated with the term, SEGS denotes a training-free, plug-and-play method for view-consistent text-to-3D generation that combats the Janus problem by extracting intermediate structural cues from a frozen diffusion U-Net, constructing a PCA-based structural subspace, and injecting the resulting energy gradient into denoising (Zhang et al., 23 Aug 2025). More broadly, the term is also relevant to adjacent energy-guided sampling paradigms in which structural or physical energy functions bias sampling dynamics, including few-step conformer generation with flow matching and learned energy models (Xu et al., 27 Dec 2025) and energy-guided dataset construction for traffic prediction via normalized interaction-energy statistics (Yang et al., 2024). This suggests that SEGS is best understood not as a single architecture class, but as a family resemblance among methods that use structural energy as a guidance signal during sampling or sample selection.

1. Definition and scope

In "Structural Energy-Guided Sampling for View-Consistent Text-to-3D" (Zhang et al., 23 Aug 2025) and the later formulation "Structural Energy Guidance for View-Consistent Text-to-3D Generation" (Zhang et al., 19 May 2026), SEGS is defined as a training-free and plug-and-play framework that improves multi-view consistency in text-to-3D generation by constructing a structural energy in the PCA subspace of U-Net features and injecting its gradient into the denoising process. The immediate target is the Janus problem, in which generated objects appear plausible from frontal views but exhibit duplicated faces, distorted backs, or inconsistent geometry from side and rear views (Zhang et al., 23 Aug 2025).

The central claim of this formulation is that viewpoint bias in 2D diffusion priors is the principal cause of Janus artifacts. Because SDS- and VSD-based text-to-3D systems rely on frozen text-to-image priors trained on viewpoint-skewed image corpora, the resulting pseudo-targets are not viewpoint-balanced; front views are overrepresented while side and back views are under-sampled (Zhang et al., 23 Aug 2025). SEGS intervenes precisely at sampling time, modifying the denoising trajectory rather than retraining the prior.

The broader relevance of the phrase "structural energy-guided sampling" extends beyond text-to-3D. In EnFlow, a flow-matching model for molecular conformer generation is coupled to an explicit learned energy model, and the energy gradient is injected into the ODE sampling dynamics to guide conformations toward lower-energy regions (Xu et al., 27 Dec 2025). In traffic prediction, an energy-guided sampling strategy uses the normalized energy distribution of smaller simulated traffic systems to construct representative training data for larger systems (Yang et al., 2024). These are not identical uses of the term, but they share the same operative principle: structural information is encoded as an energy, and sampling is biased using that energy.

2. The text-to-3D SEGS formulation

The SEGS formulation for text-to-3D is designed to sit on top of SDS or VSD pipelines rather than replace them. Standard SDS uses the diffusion model’s predicted noise to induce a gradient on 3D parameters. The paper writes the SDS gradient as

$\nabla_{\theta} \mathcal{L}_{\text{SDS} \approx \mathbb{E}_{t,\epsilon,c} \!\left[ \,\omega(t)\,\big(\epsilon_{\phi}(x_t, y) - \epsilon_t\big)\,\frac{\partial x_0}{\partial \theta} \right].$

Using the denoising identity, the clean estimate is

$\hat{x}_0^t = \frac{x_t - \sqrt{1 - \bar{\alpha}_t}\,\epsilon_{\phi}(x_t, y)}{\sqrt{\bar{\alpha}_t},$

and equivalently,

$\nabla_{\theta} \mathcal{L}_{\text{SDS} \approx \mathbb{E}_{t,\epsilon,c} \!\left[ \frac{\omega(t)}{\gamma(t)}\,(x_0-\hat{x}_0^t)\,\frac{\partial x_0}{\partial \theta} \right].$

SEGS modifies the denoising prediction rather than the 3D objective. Its generic energy-guided form is

$$\hat{\epsilon}_\phi(x_t,y)=\epsilon_\phi(x_t,y)+\lambda_v(t)\,\nabla_{x_t}E(x_t,t).$$

In the SEGS instantiation, $E$ is a viewpoint-aware structural energy $E_{\text{vp}(t)}$ defined in a PCA subspace of intermediate U-Net features (Zhang et al., 23 Aug 2025). Because DDPM/DDIM-style samplers subtract predicted noise from the state, adding the gradient to the predicted noise induces a descent step on the structural energy during denoising. The same replacement is stated to apply to VSD as well (Zhang et al., 23 Aug 2025).

A key property is that the diffusion backbone remains frozen. The method does not retrain the prior, does not add learnable parameters, and does not require multi-view 3D datasets (Zhang et al., 19 May 2026). The only intervention is the injection of a structural correction term into the sampling trajectory.

3. Construction of the structural energy

The structural energy in SEGS is built from intermediate self-attention features in the diffusion U-Net decoder. The method extracts self-attention keys from the final layer of the first decoder up-block. For each auxiliary image and denoising step $t$, the extracted feature is

$\mathbf{b}_{t,i}\in\mathbb{R}^{H\times W\times C}.$

Across $N$ samples, the features are assembled as

$$\mathbf{b}_t \in \mathbb{R}^{N\times H\times W\times C}.$$

After channel-wise mean centering, PCA is applied to obtain a low-dimensional structural basis,

$\hat{x}_0^t = \frac{x_t - \sqrt{1 - \bar{\alpha}_t}\,\epsilon_{\phi}(x_t, y)}{\sqrt{\bar{\alpha}_t},$0

with $\hat{x}_0^t = \frac{x_t - \sqrt{1 - \bar{\alpha}_t}\,\epsilon_{\phi}(x_t, y)}{\sqrt{\bar{\alpha}_t},$1 (Zhang et al., 23 Aug 2025). The retained principal components are intended to capture dominant structural directions such as silhouette, pose, and part boundaries, while suppressing incidental texture variation. This suggests that SEGS treats structure as a latent geometry-aligned representation already encoded in the pretrained U-Net rather than as an external supervisory signal.

Target-view exemplars are then obtained by augmenting the prompt with a viewpoint token such as “back view,” generating auxiliary images with the frozen diffusion model, computing CLIP similarity to the target-view text, and selecting the top-$\hat{x}_0^t = \frac{x_t - \sqrt{1 - \bar{\alpha}_t}\,\epsilon_{\phi}(x_t, y)}{\sqrt{\bar{\alpha}_t},$2 images (Zhang et al., 23 Aug 2025). If $\hat{x}_0^t = \frac{x_t - \sqrt{1 - \bar{\alpha}_t}\,\epsilon_{\phi}(x_t, y)}{\sqrt{\bar{\alpha}_t},$3 denotes the selected features, the target-view structural references are

$\hat{x}_0^t = \frac{x_t - \sqrt{1 - \bar{\alpha}_t}\,\epsilon_{\phi}(x_t, y)}{\sqrt{\bar{\alpha}_t},$4

with $\hat{x}_0^t = \frac{x_t - \sqrt{1 - \bar{\alpha}_t}\,\epsilon_{\phi}(x_t, y)}{\sqrt{\bar{\alpha}_t},$5.

At optimization time, for the current noisy render $\hat{x}_0^t = \frac{x_t - \sqrt{1 - \bar{\alpha}_t}\,\epsilon_{\phi}(x_t, y)}{\sqrt{\bar{\alpha}_t},$6, the corresponding intermediate feature $\hat{x}_0^t = \frac{x_t - \sqrt{1 - \bar{\alpha}_t}\,\epsilon_{\phi}(x_t, y)}{\sqrt{\bar{\alpha}_t},$7 is projected into the same structural basis,

$\hat{x}_0^t = \frac{x_t - \sqrt{1 - \bar{\alpha}_t}\,\epsilon_{\phi}(x_t, y)}{\sqrt{\bar{\alpha}_t},$8

The viewpoint guidance energy is defined as the average MSE between the current projected feature and the selected target-view references:

$\hat{x}_0^t = \frac{x_t - \sqrt{1 - \bar{\alpha}_t}\,\epsilon_{\phi}(x_t, y)}{\sqrt{\bar{\alpha}_t},$9

The gradient is computed via

$\nabla_{\theta} \mathcal{L}_{\text{SDS} \approx \mathbb{E}_{t,\epsilon,c} \!\left[ \frac{\omega(t)}{\gamma(t)}\,(x_0-\hat{x}_0^t)\,\frac{\partial x_0}{\partial \theta} \right].$0

The papers emphasize that $\nabla_{\theta} \mathcal{L}_{\text{SDS} \approx \mathbb{E}_{t,\epsilon,c} \!\left[ \frac{\omega(t)}{\gamma(t)}\,(x_0-\hat{x}_0^t)\,\frac{\partial x_0}{\partial \theta} \right].$1 and $\nabla_{\theta} \mathcal{L}_{\text{SDS} \approx \mathbb{E}_{t,\epsilon,c} \!\left[ \frac{\omega(t)}{\gamma(t)}\,(x_0-\hat{x}_0^t)\,\frac{\partial x_0}{\partial \theta} \right].$2 are treated as constants during optimization, so gradients do not flow through the PCA pipeline or reference construction (Zhang et al., 23 Aug 2025).

4. Sampling-time guidance, scheduling, and guards

SEGS is explicitly a sampling-time method. The modified denoising prediction is

$\nabla_{\theta} \mathcal{L}_{\text{SDS} \approx \mathbb{E}_{t,\epsilon,c} \!\left[ \frac{\omega(t)}{\gamma(t)}\,(x_0-\hat{x}_0^t)\,\frac{\partial x_0}{\partial \theta} \right].$3

Substituting this into SDS gives

$\nabla_{\theta} \mathcal{L}_{\text{SDS} \approx \mathbb{E}_{t,\epsilon,c} \!\left[ \frac{\omega(t)}{\gamma(t)}\,(x_0-\hat{x}_0^t)\,\frac{\partial x_0}{\partial \theta} \right].$4

The practical effect is to reshape the pseudo-supervision used by text-to-3D optimization so that the denoising prior is less likely to revert side and back views to frontal structure (Zhang et al., 23 Aug 2025).

Two auxiliary mechanisms are described. First, SEGS uses adaptive guidance. One formulation states $\nabla_{\theta} \mathcal{L}_{\text{SDS} \approx \mathbb{E}_{t,\epsilon,c} \!\left[ \frac{\omega(t)}{\gamma(t)}\,(x_0-\hat{x}_0^t)\,\frac{\partial x_0}{\partial \theta} \right].$5, where $\nabla_{\theta} \mathcal{L}_{\text{SDS} \approx \mathbb{E}_{t,\epsilon,c} \!\left[ \frac{\omega(t)}{\gamma(t)}\,(x_0-\hat{x}_0^t)\,\frac{\partial x_0}{\partial \theta} \right].$6 is a no-reference IQA score such as BRISQUE (Zhang et al., 23 Aug 2025). The expanded version specifies a BRISQUE-based schedule: compute BRISQUE score $\nabla_{\theta} \mathcal{L}_{\text{SDS} \approx \mathbb{E}_{t,\epsilon,c} \!\left[ \frac{\omega(t)}{\gamma(t)}\,(x_0-\hat{x}_0^t)\,\frac{\partial x_0}{\partial \theta} \right].$7, smooth with EMA,

$\nabla_{\theta} \mathcal{L}_{\text{SDS} \approx \mathbb{E}_{t,\epsilon,c} \!\left[ \frac{\omega(t)}{\gamma(t)}\,(x_0-\hat{x}_0^t)\,\frac{\partial x_0}{\partial \theta} \right].$8

normalize to $\nabla_{\theta} \mathcal{L}_{\text{SDS} \approx \mathbb{E}_{t,\epsilon,c} \!\left[ \frac{\omega(t)}{\gamma(t)}\,(x_0-\hat{x}_0^t)\,\frac{\partial x_0}{\partial \theta} \right].$9, and set

$$\hat{\epsilon}_\phi(x_t,y)=\epsilon_\phi(x_t,y)+\lambda_v(t)\,\nabla_{x_t}E(x_t,t).$$0

(Zhang et al., 19 May 2026). The intended effect is to apply stronger structural guidance early, when geometry is being established, and relax guidance later to avoid overconstraining appearance refinement.

Second, an optional Text Consistency Guard filters pseudo-supervision whose decoded $$\hat{\epsilon}_\phi(x_t,y)=\epsilon_\phi(x_t,y)+\lambda_v(t)\,\nabla_{x_t}E(x_t,t).$$1 is inconsistent with the target-view text. In the detailed formulation, a CLIP-based cosine similarity $$\hat{\epsilon}_\phi(x_t,y)=\epsilon_\phi(x_t,y)+\lambda_v(t)\,\nabla_{x_t}E(x_t,t).$$2 is computed between the pseudo-target and the view prompt; after warm-up, the threshold is

$$\hat{\epsilon}_\phi(x_t,y)=\epsilon_\phi(x_t,y)+\lambda_v(t)\,\nabla_{x_t}E(x_t,t).$$3

and supervision is discarded if $$\hat{\epsilon}_\phi(x_t,y)=\epsilon_\phi(x_t,y)+\lambda_v(t)\,\nabla_{x_t}E(x_t,t).$$4 (Zhang et al., 19 May 2026). The papers present this as auxiliary rather than central to SEGS.

5. Empirical results and ablations in text-to-3D

The text-to-3D SEGS papers evaluate on the DreamFusion prompt library using Stable Diffusion v1.4 as the main prior, 20 auxiliary “back view” images per prompt, PCA dimension $$\hat{\epsilon}_\phi(x_t,y)=\epsilon_\phi(x_t,y)+\lambda_v(t)\,\nabla_{x_t}E(x_t,t).$$5, top-$$\hat{\epsilon}_\phi(x_t,y)=\epsilon_\phi(x_t,y)+\lambda_v(t)\,\nabla_{x_t}E(x_t,t).$$6 CLIP-selected reference images, and a single NVIDIA A100 (Zhang et al., 23 Aug 2025). Two dedicated metrics are introduced.

Metric	Definition	Purpose
JR	Failures with duplicated or missing structures are manually counted over rendered views	Measures Janus-like inconsistencies
View-CS	CLIP similarity between rendered views and viewpoint phrases such as “front view,” “side view,” and “back view”	Measures view fidelity

SEGS improves both metrics across multiple baselines. For LucidDreamer, JR changes from 58.06 to 48.39 and View-CS from 30.16 to 30.95. For Magic3D, JR changes from 68.18 to 56.36 and View-CS from 32.17 to 32.85. For DreamFusion, JR changes from 72.73 to 63.64 and View-CS from 32.85 to 33.29 (Zhang et al., 23 Aug 2025). The later paper summarizes this as reducing the Janus Rate by about 10% on average while improving View-CS across baselines (Zhang et al., 19 May 2026).

A separate DreamFusion study across five seeds reports that SEGS reduces JR from 100% to 40% with SD1.4 and from 60% to 20% with SD2.1 for a sample prompt (Zhang et al., 23 Aug 2025). Qualitatively, the reported effect is fewer duplicated faces and improved back and side geometry while retaining texture detail.

The ablation results attribute the main gains to the structural guidance term rather than the guard alone. Baseline or guard-only settings retain strong front-view leakage; structural guidance alone significantly reduces Janus artifacts; structural guidance combined with the guard gives the most viewpoint-accurate results (Zhang et al., 23 Aug 2025). The top-$$\hat{\epsilon}_\phi(x_t,y)=\epsilon_\phi(x_t,y)+\lambda_v(t)\,\nabla_{x_t}E(x_t,t).$$7 study finds that $$\hat{\epsilon}_\phi(x_t,y)=\epsilon_\phi(x_t,y)+\lambda_v(t)\,\nabla_{x_t}E(x_t,t).$$8 is best, with performance deteriorating when too many references are used, plausibly because noisier or less view-specific structural targets are introduced (Zhang et al., 23 Aug 2025). The guidance-strength study reports that around $$\hat{\epsilon}_\phi(x_t,y)=\epsilon_\phi(x_t,y)+\lambda_v(t)\,\nabla_{x_t}E(x_t,t).$$9, structural correction becomes noticeable, whereas extremely large values such as $E$0 cause collapse (Zhang et al., 19 May 2026).

6. Related energy-guided sampling paradigms

Although SEGS is most specifically associated with view-consistent text-to-3D, related work shows the same structural principle in distinct domains.

In "Energy-Guided Flow Matching Enables Few-Step Conformer Generation and Ground-State Identification" (Xu et al., 27 Dec 2025), EnFlow couples a flow-matching generator to an explicit energy model and uses energy-gradient guidance during sampling. The guided vector field is written as

$E$1

with the gradient evaluated at the predicted endpoint

$E$2

The ODE update is

$E$3

starting from $E$4, where $E$5 is the Harmonic Prior (Xu et al., 27 Dec 2025). The method emphasizes that standard diffusion-style guidance does not directly transfer because the flow-matching path is non-Gaussian, and the endpoint-based gradient is therefore essential. In GEOM-QM9 and GEOM-Drugs, EnFlow improves few-step conformer generation and enables energy-based ranking for ground-state identification (Xu et al., 27 Dec 2025).

In "Energy-Guided Data Sampling for Traffic Prediction with Mini Training Datasets" (Yang et al., 2024), the term SEGS is not used explicitly, but the paper operationalizes an energy-guided structural sampling idea. Traffic states on a ring road are represented by $E$6, with forward-looking neighborhood

$E$7

and local energy

$E$8

with distance-dependent interaction

$E$9

The key empirical claim is that normalized energy distributions for system sizes 30, 60, 120, 240, and 600 sites are similar, implying scale invariance sufficient to use smaller-system simulations as proxies for larger-system training data (Yang et al., 2024). This is not sampling-time guidance in a denoiser, but it is a structurally informed energy-based sampling rule.

These related formulations indicate a recurring design pattern: a learned or modeled energy encodes structural regularity, and the gradient or distributional statistics of that energy guide generation or data selection.

7. Conceptual significance, distinctions, and limitations

SEGS differs from retraining-based or architecture-modifying approaches by operating entirely at inference or optimization time. In text-to-3D, it does not introduce extra control networks, additional 3D supervision, or diffusion-weight updates (Zhang et al., 19 May 2026). This makes it compatible with existing SDS/VSD pipelines, including DreamFusion-like systems, as a guidance module rather than a replacement objective (Zhang et al., 23 Aug 2025).

It also differs from generic diffusion guidance in where and how structure is encoded. The structural energy is not a classifier score or a pixel-space penalty. It is computed in a PCA subspace of intermediate self-attention features, which the papers argue retain spatially aligned structure while avoiding the overconstraint that direct image-space losses might impose (Zhang et al., 23 Aug 2025). A plausible implication is that SEGS belongs to a broader class of internal-feature guidance methods, but its distinguishing feature is the explicit construction of a view-specific energy over a learned structural subspace.

Several misconceptions are addressed implicitly by the reported analysis. One is that uniform camera sampling alone should solve Janus artifacts. The SEGS papers argue that this is insufficient because the bias enters through the 2D diffusion prior’s denoising direction rather than the camera distribution itself (Zhang et al., 19 May 2026). Another is that multi-view consistency necessarily requires retraining on specialized datasets. SEGS is presented as evidence that frozen priors already contain usable structural signals, provided that sampling is guided appropriately (Zhang et al., 23 Aug 2025).

The limitations are also domain-specific and nontrivial. In text-to-3D, failure cases persist around front-side transition angles, where residual frontal cues can remain along lateral contours (Zhang et al., 23 Aug 2025). The reported explanation is twofold: ambiguity in side-view evidence in the frozen 2D prior and weaker structural targets for intermediate azimuths when the reference set focuses on back views (Zhang et al., 19 May 2026). In the traffic setting, the method is presented as proof of concept and does not establish definitive superiority over all competing predictors (Yang et al., 2024). In the molecular setting, the guidance scheme is tied to non-Gaussian path flow matching and few-step ODE sampling, so its transferability to unrelated sampling regimes is not established (Xu et al., 27 Dec 2025).

Taken together, Structural Energy-Guided Sampling denotes a technically specific text-to-3D method and, more broadly, a methodological motif in which structural energy is elevated from a passive scoring function to an active guidance signal. In that sense, SEGS marks a shift from post hoc evaluation of structure to direct trajectory shaping by structural criteria during sampling itself (Zhang et al., 23 Aug 2025).