StereoSpace: Unified Spatial Framework

Updated 18 December 2025

StereoSpace is a unified framework that encodes spatial attributes of sound sources, viewpoints, and spacetime events into a canonical coordinate system.
It employs both implicit and explicit spatial embeddings to enhance audio generation, source separation, and stereo vision synthesis through precise spatial manipulation.
The framework integrates rigorous mathematical formalisms and advanced perceptual metrics to quantitatively assess and improve spatial realism in diverse applications.

StereoSpace represents a unifying principle and operational framework for the analysis, synthesis, and manipulation of spatial information across stereo modalities, including audio, vision, and even relativistic spacetime. Across domains, the notion of “StereoSpace” denotes a latent or explicit coordinate system in which core spatial variables—location or direction of sources, observer viewpoints, and propagation geometry—are encoded, manipulated, and made accessible to models or users for tasks such as audio generation, source separation, upmixing, spatialized sound design, and spacetime localization.

1. Theoretical Foundations of StereoSpace

StereoSpace as a technical construct fundamentally refers to the establishment of a reference frame—a canonical coordinate system—wherein the spatial attributes of entities (sound sources, viewpoints, spacetime events) are represented explicitly for subsequent manipulation or inference. In audio, vision, and physics, StereoSpace enables controlled and interpretable spatial reasoning.

In the relativistic setting, the term “stereometric coordinates” formalizes a system for spacetime localization based on a five-satellite protocol. Here, StereoSpace is defined as the coordinate chart $\sigma(e) = (\tau_e^1,\tau_e^2,\tau_e^3,\tau_e^4, \mathring{\tau}_e)$ , derived from the intersection structure of null cones supplemented by projective angular data from satellite celestial spheres. This coordinate system is intrinsic, conformally invariant, and admits projective (Cartan) structure, generalizing classic parallax to all of spacetime (Rubin, 2014).

In learned audio-visual systems, StereoSpace is induced either implicitly (via model architectures sensitive to inter-channel cues) or explicitly (via spatial embeddings, conditioning inputs, or learned spatial fields), permitting spatial control and evaluation.

2. StereoSpace in Audio: Synthesis, Separation, and Manipulation

Recent advances establish StereoSpace as the operating domain for spatially-aware audio generation. Models such as SAGM (Li et al., 2023) and FoleySpace (Zhao et al., 18 Aug 2025) treat the mapping from mono to stereo (binaural) as a conditional generation process informed by auxiliary spatial signals:

In visually guided synthesis, spatial context is encoded from framewise object locations, monocular depth, or multi-modal embeddings, and then mapped to a 2D or 3D trajectory representing the source’s position over time. This trajectory, together with the mono (or coarse) input, forms the effective coordinate in the model’s StereoSpace for binaural rendering.
Diffusion models condition on such spatial trajectories, with spatial consistency achieved via the injection of 3D coordinates at every step of the UNet or denoising network. In FoleySpace, sound source 2D coordinates and depth are mapped to 3D trajectories $(x_k,y_k,z_k)$ centered on the listener, then used as conditioning for binaural audio synthesis with a modified DiffWave backbone (Zhao et al., 18 Aug 2025).

2.2 StereoSpace for Source Separation and Control

SpaIn-Net (Petermann et al., 2022) exemplifies the use of “stereophonic location,” e.g., panning angle $\alpha_k$ , to condition neural networks for instrument separation in stereo mixtures. The spatial conditioning either concatenates, adds, or AdaIN-fuses panning-derived embeddings into the network, forming a StereoSpace of latent spectral features jointly modulated by explicit spatial directives. This approach enables:

Improved source disentanglement, particularly for same-class sources occupying distinct spatial positions, as shown by multi-guitar separation when each receives its own spatial stream.
Increased robustness to errors in user-supplied conditioning, as the model can recover implicit spatial cues from stereo channel content.

In Sep-Stereo (Zhou et al., 2020), the architectural fusion of association pyramids for visual–audio mapping also forms a “StereoSpace” where spatial source positions (inferred from image regions) align with corresponding audio signals, allowing stereo generation and separation to be trained as complementary tasks with a shared backbone.

2.3 StereoSpace for Ambience Decomposition and Upmixing

“Geometrically Motivated Primary-Ambient Decomposition” (Paulus et al., 2022) encodes the stereo scene as samples of a 2D spatial field, then applies adaptive rotations to recenter primary energy and MMSE-based Wiener filtering for center-channel extraction. This process constructs a latent StereoSpace representation where channels can be re-scaled or re-mapped for upmixing, e.g., to 5.1/7.1 layouts.

3. StereoSpace in Vision: Depth-Free Stereo Synthesis

The “StereoSpace” approach extends beyond audio, providing a learning-based coordinate system for geometry-aware visual synthesis (Behrens et al., 11 Dec 2025):

The StereoSpace framework for monocular-to-stereo conversion canonicalizes all training pairs into a rectified coordinate frame, eliminating camera pose variability and enabling the network to focus on modeling true stereo disparities and occlusions.
Viewpoint information is encoded as dense Plücker ray maps per pixel; these maps, injected as conditioning into a dual-UNet latent diffusion model, establish the StereoSpace for end-to-end stereo view generation.
By training in this canonical space and refraining from explicit depth estimation or proxy geometry during inference, the model attains superior performance on parallax, occlusions, and multi-layered or non-Lambertian phenomena compared to warp-and-inpaint or depth-based alternatives.

4. StereoSpace in Relativistic Spacetime and Mathematical Geometry

Rubin (Rubin, 2014) introduces a mathematically rigorous theory of stereometric coordinates based on relativistic localizing systems:

A five-satellite constellation provides sufficient data (emission timestamps and angles) to assign unique stereometric coordinates to any spacetime event, which rely solely on the conformal and projective structures underlying null cone intersections and celestial sphere observations.
Space–time parallax is generalized, with parallax differentials among satellite observations entering birational expressions for coordinates.
Transition maps between stereometric charts are fractional-linear ( $PGL(5,\mathbb{R})$ ), and the entire system encodes a local projective Cartan geometry over spacetime, with structure and curvature determined by the constellation.

5. Quantification, Metrics, and Control in StereoSpace

To evaluate and operate within StereoSpace, task-appropriate metrics and control signals are defined:

For audio generation, perceptual and spatial metrics such as the SPL-difference trajectory (Li et al., 2023), Perceived Spatiality Score, objective distances (Fréchet, KL), and direction-aligned mean absolute errors quantify spatial realism and localization.
In vision-driven binaural synthesis, the alignment of generated spatial trajectories with ground-truth 3D paths is evaluated both objectively (audio feature distances, TDOA error) and subjectively (listener MOS, event relevance, direction accuracy).
In monocular-to-stereo synthesis, metrics such as iSQoE (perceptual comfort) and MEt3R (multi-view geometric consistency) are used, with the evaluation pipeline strictly excluding geometric leakage by prohibiting ground-truth or proxy geometry at inference (Behrens et al., 11 Dec 2025).

Model design choices—such as spatially-aware embeddings, adaptive fusion, and consistent coordinate mapping—directly affect performance within the defined StereoSpace, as confirmed by large-scale ablation and user studies.

6. Limitations, Domain-Specific Extensions, and Future Work

Current realizations of StereoSpace are bound by the following constraints:

In audio, most contemporary systems model only azimuthal (left–right) localization; elevation, distance cues, and listener/head-transfer variability (HRTF) remain underexplored (Zhou et al., 2020, Sun et al., 14 Oct 2024, Zhao et al., 18 Aug 2025).
Vision-based approaches typically assume static listener orientation and do not model dynamic listener movements or personalized HRTFs.
In relativistic systems, practical deployment would require precise time synchronization and robust angular measurement protocols among satellites.

Extensions under discussion include:

Elevation and multi-channel extensions (ambisonics, 5.1/7.1+ systems), higher-order spatial cues, and interactive region-of-interest selection (Petermann et al., 2022, Sun et al., 14 Oct 2024).
Improved fusion of textual, visual, and spatial controls, curriculum learning for complex captions, and domain adaptation to wild or real-world text/image–audio pairs (Sun et al., 14 Oct 2024).
Integration of dynamic listener tracking and personalized stereo fields via head-tracking or individual HRTF adaptation (Li et al., 2023, Zhao et al., 18 Aug 2025).
In mathematical geometry and relativistic physics, computation of the Cartan/projective curvature and study of the global trivializability of the StereoSpace coordinate system (Rubin, 2014).

7. Summary Table: Domains and Methods of StereoSpace

Application Domain	StereoSpace Construction	Key Metrics/Evaluation
Audio Synthesis (Binaural)	Spatial trajectories + conditioned diffusion	SPL-diff, Perceived Spatiality, FD, SA
Source Separation	Panning angle embeddings, APNet	SI-SDR gain, SDR/SAR/SIR, user study
Vision (Stereo Image Synthesis)	Canonical rectified frame, Plücker embedding	iSQoE, MEt3R, qualitative parallax
Audio-Visual Fusion	Coarse-to-fine associative visual–audio fusion	STFT/env distance, MOS, A/V sync error
Relativistic Geometry	5-satellite protocol, projective coordinates	Intrinsic, causal, conformal validity

StereoSpace, as reflected in these works, provides a principled coordinate system for spatial manipulation, inference, and control across diverse fields, unifying geometric, physical, and machine learning perspectives for stereo-related research and applications (Petermann et al., 2022, Paulus et al., 2022, Li et al., 2023, Sun et al., 14 Oct 2024, Zhao et al., 18 Aug 2025, Behrens et al., 11 Dec 2025, Rubin, 2014).