SpheRoPE: Zero-Shot 360° Panoramas

• SpheRoPE is a zero-shot framework that enforces spherical geometric priors to generate equirectangular 360° images without retraining.
• It partitions rotary position embeddings into cyclic and spherical components and introduces a three-way classifier-free guidance strategy for spatial accuracy.
• The method achieves high-fidelity panoramas with reduced seams and improved global topology, as demonstrated by superior metrics on benchmark datasets.

SpheRoPE is a zero-shot, optimization-free framework for generating 360° panoramic images and videos by directly imposing spherical geometric priors on pre-trained diffusion transformers. The SpheRoPE method achieves seamless, high-fidelity equirectangular panoramas without retraining or per-image optimization, addressing fundamental topological constraints of the equirectangular projection (ERP) that standard generative models typically fail to respect. Through a dual-path reparameterization of rotary position embeddings (RoPE) and a novel three-way classifier-free guidance strategy, SpheRoPE generalizes across multiple architectures, modalities, and conditioning pipelines while operating entirely as an inference-time adaptation (Hirschorn et al., 30 Jun 2026).

1. Equirectangular Panoramas and Motivations

A 360° panorama in computer vision is conventionally mapped via equirectangular projection (ERP), transforming spherical $(\theta,\,\varphi)$ into a 2D rectangular image $x\in\mathbb{R}^{H\times W\times 3}$, where $W=2H$, $\theta\in[-\pi/2,\pi/2]$, and $\varphi\in[-\pi,\pi)$. ERP imposes two strict structural constraints:

• Horizontal periodicity: $x[r,c]=x[r,c\mod W]$ for all $r$, requiring the image to wrap seamlessly.
• Polar convergence: $x[0,c_1]=x[0,c_2]$ and $x[H-1,c_1]=x[H-1,c_2]$ for all $c_1,\,c_2$, enforcing that all longitudes converge at the poles.

Contemporary diffusion transformers employing RoPE are designed for flat Euclidean grids and exhibit visible seams and fractured poles when applied to ERP panoramas. Prior approaches either require full dataset-level fine-tuning (e.g., LoRA, spherical convolutions) or iterative optimization (e.g., patch-stitching, warping plus inpainting), which have limited generalization, high computational cost, or prohibitive inference latency (10s–1000s of seconds per image).

SpheRoPE exploits the observation that pre-trained diffusion transformers possess some panoramic priors but lack the precise ERP topological constraints. Its objective is to rectify these deficiencies at inference time, ensuring seamless and geometrically correct panoramas without any retraining or fine-tuning.

2. Zero-Shot, Inference-Time Framework

SpheRoPE acts as a plug-in module for arbitrary diffusion transformer backbones that employ RoPE, modifying only the width-axis embeddings to impose spherical geometry. The method further introduces Semantic Distortion Classifier-Free Guidance (SD-CFG)—a three-branch, prompt-anchored fusion strategy—to steer the generative process toward topologically valid ERP outputs.

A typical text-to-panorama workflow comprises:

1. Tokenizing a user prompt $x\in\mathbb{R}^{H\times W\times 3}$0 and forming an anchored prompt $x\in\mathbb{R}^{H\times W\times 3}$1 where $x\in\mathbb{R}^{H\times W\times 3}$2 is a brief geometric descriptor (e.g., “equirectangular panorama with seamless wrap-around and pole convergence”).
2. At each denoising step $x\in\mathbb{R}^{H\times W\times 3}$3:
   • Replacing standard RoPE with SpheRoPE along the width axis.
   • Executing three parallel network passes: unconditional ($x\in\mathbb{R}^{H\times W\times 3}$4), semantic ($x\in\mathbb{R}^{H\times W\times 3}$5), and geometric ($x\in\mathbb{R}^{H\times W\times 3}$6, conditioned on $x\in\mathbb{R}^{H\times W\times 3}$7).
   • Combining results via SD-CFG fusion:

   $x\in\mathbb{R}^{H\times W\times 3}$8

• Applying the standard DDPM update.

1. Decoding the final latent $x\in\mathbb{R}^{H\times W\times 3}$9 using a VAE decoder with circular latent padding to ensure seam-free output.

This pipeline requires no retraining and is optimization-free per image. All backbone weights and conditioning mechanisms are preserved.

3. Spherical RoPE: Spectral Partitioning of Position Embeddings

Standard RoPE on the width axis computes angle rotations as $W=2H$0 with frequencies $W=2H$1, which fail to enforce $W=2H$2-periodicity or polar convergence, thus violating ERP constraints. SpheRoPE partitions the RoPE channels into high-frequency and low-frequency components via a data-driven index $W=2H$3 determined by harmonicity thresholds ($W=2H$4 or $W=2H$5 with $W=2H$6):

• High-frequency channels ($W=2H$7): employ cyclic linear encoding. Each channel is snapped to the nearest harmonic, and the frequency is set as $W=2H$8, enforcing exact $W=2H$9 periodicity. This yields perfect wrap-around (satisfying ERP horizontal periodicity, C1) and crisp local textural features.
• Low-frequency channels ($\theta\in[-\pi/2,\pi/2]$0): use spherical Cartesian encoding. The coordinates $\theta\in[-\pi/2,\pi/2]$1 are mapped to spherical angles $\theta\in[-\pi/2,\pi/2]$2 and then to Cartesian points $\theta\in[-\pi/2,\pi/2]$3 on the unit sphere $\theta\in[-\pi/2,\pi/2]$4:

$\theta\in[-\pi/2,\pi/2]$5

The $\theta\in[-\pi/2,\pi/2]$6 vectors are injected in the low-frequency RoPE slots, guaranteeing both ERP constraints—horizontal periodicity via the longitude loop, and polar convergence via $\theta\in[-\pi/2,\pi/2]$7 for poles.

Only the width axis RoPE is altered; height and, for video, temporal axes remain unchanged. The scaling parameter $\theta\in[-\pi/2,\pi/2]$8 ensures consistency with the pre-trained model’s numerical regime.

4. Semantic Distortion Classifier-Free Guidance (SD-CFG)

SD-CFG generalizes standard classifier-free guidance (CFG) by introducing a third, geometrically anchored branch. Standard CFG fuses unconditional and semantic predictions as $\theta\in[-\pi/2,\pi/2]$9. SD-CFG includes a geometric branch by using an appended prompt $\varphi\in[-\pi,\pi)$0 and fusing:

$\varphi\in[-\pi,\pi)$1

with $\varphi\in[-\pi,\pi)$2 and $\varphi\in[-\pi,\pi)$3. This decomposition enables explicit control of semantic and geometric correction, reducing seams and polar distortions while retaining fine semantic granularity. SD-CFG requires $\varphi\in[-\pi,\pi)$4 more network passes per step.

5. Integration and Experimental Results

SpheRoPE and SD-CFG are compatible with multiple diffusion transformer backbones without weight updates or architectural modifications. Demonstrated integrations include:

• Flux.1: static text-to-image generation.
• Flux.2: a larger, static backbone.
• LTX-Video 2.3: joint audio-video diffusion.

Typical settings: 1024×2048 ERP, 50 denoising steps, harmonic tolerance $\varphi\in[-\pi,\pi)$5, radius $\varphi\in[-\pi,\pi)$6, SD-CFG $\varphi\in[-\pi,\pi)$7, default $\varphi\in[-\pi,\pi)$8 per backbone, and circular latent padding in the VAE decoder.

On the ODI-SR dataset (1,200 test panoramas with captions), SpheRoPE (Flux.2 backbone) achieves superior panorama-level FAED (360-FID) of 25.4 and discontinuity score (DS) of 0.94, outperforming or equaling fine-tuned and LoRA methods on global coherence and multi-view realism. For 360° video, LTX-Video 2.3 with SpheRoPE attains near state-of-the-art across MUSIQ, CLIP-Mean, temporal flicker, motion smoothness, and subject/background consistency, with inference latency ~$\varphi\in[-\pi,\pi)$9 s/frame (compared to 50 s/frame for baseline optimization methods).

In human preference studies (320 pairwise comparisons), Flux.2 results are preferred $x[r,c]=x[r,c\mod W]$0 of the time versus baselines, both for overall quality and textual alignment.

Plug-and-play conditioning is preserved; image-to-panorama and audio-video modalities are supported out-of-the-box given the absence of weight changes.

6. Ablation and Sensitivity Analyses

Comprehensive ablations elucidate individual and joint effects:

• Component ablation: Standard Flux.2 with RoPE+CFG yields FAED=33.4, DS=1.37; adding only SpheRoPE erases seams (DS→0.92, FAED 40.9), only SD-CFG improves global realism (FAED→27.4, DS=1.22), while SpheRoPE+SD-CFG achieves optimal (FAED=25.4, DS=0.94).
• Cyclic vs. Spherical encoding: Only cyclic yields perfect wrap but global artifacts; only spherical Cartesian produces good poles but blurry textures; the dual-path configuration yields both crisp local features and valid global topology.
• Harmonic tolerance ($x[r,c]=x[r,c\mod W]$1): Too small ($x[r,c]=x[r,c\mod W]$2) leads to few cyclic channels and blur; higher values saturate results.
• SD-CFG strength ($x[r,c]=x[r,c\mod W]$3): Lower $x[r,c]=x[r,c\mod W]$4 favors local realism; higher $x[r,c]=x[r,c\mod W]$5 enhances global coherence, with stable trade-off over $x[r,c]=x[r,c\mod W]$6.
• CFG scheduling: Early application of $x[r,c]=x[r,c\mod W]$7 is crucial to enforce ERP geometry.
• Radius scaling ($x[r,c]=x[r,c\mod W]$8): $x[r,c]=x[r,c\mod W]$9 is optimal, with deviations leading to distortions.
• Prompt engineering: Minimal $r$0 under-specifies geometry; overly verbose descriptors over-distort. The default prompt balances both.
• VAE padding: Replacing zero-padding with circular latent padding in the VAE eliminates boundary seams with no computational cost increase.

7. Limitations and Future Directions

SpheRoPE presents certain limitations:

• Failure cases include hallucination of flat seams for strong perspective cues or filling with repeating structures.
• The backbone must support RoPE; models with learned or additive position codes require new adaptation.
• Success depends on the presence of panorama-like data in the backbone's pre-training distribution.
• Video extension is presently limited to static cameras; maintaining ERP topology with moving cameras remains unsolved.
• Three-branch SD-CFG increases inference cost by $r$1.

Proposed future directions include incorporation of spatialized audio for 360° videos, broadening RoPE generalizations to other non-Euclidean manifolds (cylindrical, hyperbolic, or learned geometries), and the development of training-free geometric adapters for broader generative modeling contexts (Hirschorn et al., 30 Jun 2026).

SpheRoPE exemplifies a training- and optimization-free methodology that spectrally partitions RoPE into cyclic and spherical bands, leverages a three-way semantic-geometric guidance, and preserves all backbone weights and conditioning procedures—collectively achieving seamless, high-quality 360° panorama and video generation on state-of-the-art diffusion transformers.