Neural Emission Fields

• Neural Emission Fields (NEFs) are neural implicit representations that model direct lighting from complex emitters by precomputing the receiver-side direct-lighting integral and using a single neural network evaluation per shading point, enabling real-time rendering with intrinsic visibility and illumination.
• NEFs excel for emitters with complex geometries and internal reflections, where analytical methods are less accurate or slower, ensuring consistent performance despite emitter complexity and only dependent on the complexity of the field.
• Instances in various scenes can be generated implicitly in real time, with efficient runtime costs that scale linearly with the number of independent emitters, making NEFs versatile and portable.

Neural Emission Fields (NEF) are neural implicit representations that map receiver-side geometric and material configurations, expressed in an emitter-local coordinate frame, to the direct outgoing radiance produced by a complex emitter. In the formulation introduced in “Real-time Rendering of Pre-integrated Neural Emitters” (Coomans et al., 5 Oct 2026), an NEF precomputes the complete receiver-side direct-lighting integral, including emitter-internal transport, and replaces runtime integration with a single neural-network evaluation per shading point. The term NEF is not universal: “Neural Acoustic Fields” (Luo et al., 2022), “Neural Edge Fields” (Ye et al., 2023), and “Neural Brain Fields” (Kedem et al., 20 Dec 2025) use related neural-field ideas but denote different representations rather than the emitter-anchored lighting model.

1. Definition and conceptual basis

An NEF represents the direct outgoing radiance reflected by a receiver due to a particular emitter. Its canonical mapping is

$$D_\theta(\tilde{x},\tilde{n},\tilde{\omega}_o,\alpha) \approx L_o(x,\omega_o),$$

where $x$ is the receiver position in world space, $n$ is the receiver normal, $\omega_o$ is the outgoing or viewing direction, $\alpha$ is the GGX roughness parameter, and the tilded quantities are expressed in the emitter’s local coordinate frame. The network parameters are denoted by $\theta$.

The field is therefore receiver-aware rather than solely an encoding of emitter appearance. Its output depends on receiver position, receiver orientation, receiver viewing direction, and receiver material. The principal training configuration uses GGX materials with $\alpha\in[0.1,1]$. A useful characterization is:

$$(\text{position},\text{normal},\text{view direction},\text{material}) \longmapsto \text{emitter-induced outgoing radiance}.$$

The defining operation is pre-integration. Conventional direct illumination evaluates an integral over incident directions,

$$L_o^{\mathrm{direct}}(x,\omega_o) = \int_{\Omega} f_r(x,\omega_i,\omega_o) L_i^{\mathrm{emitter}}(x,\omega_i) (\omega_i\cdot n)\,d\omega_i.$$

For complex emitters, $L_i^{\mathrm{emitter}}$ may itself contain internal transport through occluding housings, apertures, self-occlusion, internal reflections, and multiple bounces. An NEF learns the result of this entire integral:

$x$0

Thus, the emitter assembly, its internal light transport, the receiver BRDF, and the near-field illumination response are absorbed into the learned field during offline training.

The representation is distinct from a conventional neural radiance field. A NeRF generally represents scene appearance or view-dependent radiance and uses volumetric ray integration. An NEF is anchored to an emitter and predicts a pre-integrated illumination response in the volume around it. It is also distinct from a proxy emitter representation: a proxy may precompute outgoing emitter radiance, but the receiver must still sample and integrate that proxy at runtime.

2. Emitter complexity and the motivation for pre-integration

Real emitters may contain occluding housings around filaments or LEDs, thousands or millions of emissive-mesh polygons, spatially varying or textured emission, non-convex geometry, internal reflections and multiple light bounces, and deforming or time-varying components. These characteristics make direct runtime integration expensive.

Analytical area-light methods, including polygonal form-factor solutions and Linearly Transformed Cosines, are effective for simple planar emitters but generally assume simplified geometry, radiance, or BRDF distributions. Their evaluation cost scales approximately as $x$1 for an emitter with $x$2 vertices. Their approximation error increases for glossy receivers, textured emission, non-planar sources, and non-convex assemblies. The reported crossover for glossy shading is approximately 267 emitter vertices.

At $x$3, the reported runtimes are:

Method	Quad, 4 vertices	Stanford Dragon, $x$4 vertices
Analytical diffuse	$x$5 ms	$x$6 ms
LTC glossy	$x$7 ms	$x$8 ms
NEF diffuse	$x$9 ms	$n$0 ms
Glossy NEF	$n$1 ms	$n$2 ms

NEF is slower than analytical methods for a tiny quad, but its inference cost is independent of emitter polygon count. The cost instead depends on the complexity of the learned radiance field.

Monte Carlo and many-light methods can handle arbitrary emitters, but finite sampling produces variance and requires runtime samples, BSDF evaluations, visibility tests, temporal or spatial reuse, and often denoising. In a Cornell-box experiment with 1000 point lights combined into one composite emitter, ReSTIR required approximately 256 samples per pixel without denoising, or 32 samples per pixel with denoising, to reach an error comparable to a single NEF query.

Proxy methods remove emitter-side path tracing at runtime but retain receiver-side integration. NEF moves this integration offline. In the reported proxy comparison, even an ideal oracle proxy with free, noise-free radiance queries required approximately 734 proxy samples per pixel on the pierced-sphere scene to match one NEF query when using learned importance sampling.

3. Representation and diffuse/glossy architecture

The NEF uses two output heads: a diffuse head and a glossy or specular head. Its predicted radiance is

$n$3

where $n$4 and $n$5 are the receiver’s diffuse and glossy albedo or texture, $n$6 and $n$7 are learned responses, and $n$8 is the reflected outgoing direction. The reflected direction is

$n$9

Factoring out receiver textures allows the network to represent illumination responses without memorizing every possible albedo pattern. For a purely diffuse receiver, the glossy head can be omitted.

The architecture uses a multiresolution hash encoding of position, a multiresolution hash encoding of reflected direction for glossy appearance, the surface normal, and roughness for the glossy head. Each head uses four fully connected layers of width 128 with ReLU activations and a linear RGB output. The hash-grid configuration uses eight levels, a level-size growth factor of $\omega_o$0, four-float latent vectors, and $\omega_o$1 hash entries. Reported half-precision memory is 15.22 MB for the diffuse NEF and 30.46 MB for the glossy NEF.

Encoding reflected direction rather than raw outgoing direction aligns the representation with specular highlights. The reported ablations give the following perceptual $\omega_o$2 errors:

Variant	$\omega_o$3	$\omega_o$4	$\omega_o$5
Full two-head NEF	0.0216	0.0230	0.0172
Encode $\omega_o$6 instead of reflected direction	0.0299	0.0269	0.0222
Single head	0.0359	0.0302	0.0249
Single head, doubled MLP	0.0324	0.0252	0.0204
Decoupled position hash grids	0.0246	0.0240	0.0195

The two-head factorization improves quality for comparable capacity, while decoupling the position hash grids provides little quality benefit despite the additional capacity.

The high dimensionality of the input domain motivates a neural representation rather than a conventional grid. A glossy field depends approximately on three position dimensions, two normal dimensions, two reflected-direction dimensions, and one roughness dimension, yielding an eight-dimensional domain before adding time. A grid with 32 samples per dimension would require $\omega_o$7 entries.

4. Offline training and encoded transport

Training samples are generated in the emitter’s local coordinate system. Receiver positions are sampled uniformly within an emitter-space bounding box. For the glossy head, the query consists of

$\omega_o$8

The normal is sampled so that the emitter is visible in the normal’s hemisphere, the outgoing direction is sampled uniformly over the upper hemisphere about the normal, and roughness is sampled according to

$\omega_o$9

The diffuse head uses only $\alpha$0. For deformable or animated emitters, time is appended:

$\alpha$1

Time is encoded using an eight-band Fourier encoding.

Targets are generated by offline path tracing against the actual emitter assembly. Standard next-event estimation is sufficient for simple bare emissive surfaces. Emitters with housing geometry, self-occlusion, or internal reflection require full path tracing inside the emitter assembly. The target is a Monte Carlo estimate of direct outgoing radiance,

$\alpha$2

with a default of $\alpha$3 samples per radiance estimate. Quality improvements diminish beyond 64 samples, although difficult emitters such as the pierced sphere may require much larger offline reference renders for evaluation.

The training targets are generated on the fly rather than stored as a cache. Training uses Adam, an initial learning rate of $\alpha$4, batch size $\alpha$5, and cosine learning-rate decay. The loss is a relative $\alpha$6 objective:

$\alpha$7

where $\alpha$8 denotes stop-gradient. Relative normalization prevents bright parts of the field from dominating training and allocates capacity across the emitter-space.

Reported training times range from approximately one minute for a simple diffuse quad to roughly three hours for difficult emitters involving internal interreflections or temporal variation. Representative budgets include 10,000 iterations and one minute for a diffuse quad, 100,000 iterations and 12 minutes for the Dragon, 250,000 iterations and 48 minutes for a dynamic flag, and 500,000 iterations and approximately two hours 41 minutes for a pierced sphere with interreflection.

The learned field can absorb emitter-internal phenomena without explicit runtime geometric evaluation. These include occluding housings, self-occlusion, internal interreflections, spatially varying emission, high-polygon meshes, and predefined deformations. For deformable emitters, the deformation family must be represented during training.

5. Runtime rendering, portability, and visibility

At runtime, the renderer obtains the G-buffer configuration $\alpha$9. For each emitter instance, the configuration is transformed into the emitter’s local frame and evaluated once:

$\theta$0

The receiver’s diffuse and glossy albedos are applied, and the result is accumulated with contributions from other emitters. The NEF evaluation performs no runtime integration over emitter geometry, proxy sampling, importance sampling, BSDF loop, Monte Carlo estimator for the emitter contribution, or denoising of the NEF illumination itself.

The field is portable under rigid transformations because it is trained in a canonical emitter-local frame. If $\theta$1 is the emitter-to-world transformation, then

$\theta$2

For the rotational component $\theta$3,

$\theta$4

The network weights remain unchanged as the emitter moves. A trained NEF can therefore be translated, rotated, uniformly scaled, reused in multiple scenes, and instantiated multiple times. Non-uniform scaling and shearing are not supported because they distort the learned spatial and angular distributions.

The field is trained within a finite axis-aligned emitter-space bounding region extending to approximately 20 times the emitter’s largest extent on each axis. Outside this region, an optional analytical extension clamps the query to the nearest boundary point and applies inverse-square scaling:

$\theta$5

NEF inherently captures visibility within the emitter assembly, including self-occlusion, housing occlusion, internal apertures, and internal interreflection. It does not capture arbitrary external scene geometry. External visibility can be added with a shadow map, a shadow ray, a small stochastic visibility budget, or a ratio estimator combining deterministic NEF lighting with stochastic visibility. The runtime decomposition is therefore approximately

$\theta$6

For soft visibility, $\theta$7 may be estimated stochastically or through denoising. The field is consequently an unoccluded direct-illumination representation rather than a complete scene-wide visibility solution.

For $\theta$8 independent emitters, the current implementation evaluates and sums $\theta$9 NEFs:

$\alpha\in[0.1,1]$0

Runtime cost is therefore linear in the number of distinct emitter fields, although several nearby emitters may potentially be trained as one composite NEF.

6. Evaluation, limitations, and terminology

For a uniform planar emitter and diffuse receiver, NEF matches the analytical form-factor reference closely, with a reported perceptual $\alpha\in[0.1,1]$1 error of 0.0041. For glossy receivers, NEF improves over LTC across the evaluated roughness values:

Roughness $\alpha\in[0.1,1]$2	LTC $\alpha\in[0.1,1]$3	NEF $\alpha\in[0.1,1]$4
0.10	0.0459	0.0188
0.30	0.0716	0.0169
0.50	0.0470	0.0149
0.70	0.0271	0.0128
0.90	0.0191	0.0125

Experiments with a bare emissive Stanford Dragon, a pierced sphere with an internal filament, and a lattice box housing a spherical emitter show that the field can reproduce softening through apertures, brightening from internal reflection, spatial redistribution of emitted radiance, and directional self-occlusion. Textured and colored emitters require no architectural change. A time-conditioned NEF evaluated on a textured fireball reported $\alpha\in[0.1,1]$5 values of 0.0525, 0.0599, and 0.0358 across multiple frames.

Representative full-scene results include $\alpha\in[0.1,1]$6 for Sponza, $\alpha\in[0.1,1]$7 for Bistro, $\alpha\in[0.1,1]$8 for Neon NEF, $\alpha\in[0.1,1]$9 for Whiteroom, and $$(\text{position},\text{normal},\text{view direction},\text{material}) \longmapsto \text{emitter-induced outgoing radiance}.$$0 for Living Room. Bistro contains six instances of one pierced-sphere emitter at different locations and orientations, demonstrating portability.

At full HD on an RTX 4090, inference requires 1.2 ms for a diffuse NEF and 2.5 ms for a glossy NEF. The method’s standard models require approximately 15 MB per diffuse emitter and 30 MB per glossy emitter. These costs are largely independent of whether the emitter has four vertices or 436,000 vertices.

The principal failure mode for glossy rendering occurs as $$(\text{position},\text{normal},\text{view direction},\text{material}) \longmapsto \text{emitter-induced outgoing radiance}.$$1, where near-mirror materials produce extremely sharp spatial and angular highlights. A separate experiment trained down to $$(\text{position},\text{normal},\text{view direction},\text{material}) \longmapsto \text{emitter-induced outgoing radiance}.$$2 and observed increasing perceptual error near mirror-like conditions. Other limitations include external-scene occlusion, arbitrary independent motion of emitter components, inefficient supervision for heavily enclosed emitters or narrow apertures, training costs for difficult fields, finite-domain behavior, and limited generalization to emitter geometries or deformation families absent from training. The current method also scales linearly with the number of independent emitters.

The acronym NEF is context-dependent. In the emitter-rendering literature, it denotes Neural Emission Field, a pre-integrated, emitter-anchored lighting representation (Coomans et al., 5 Oct 2026). In “Learning Neural Acoustic Fields,” NAFs are continuous neural representations of scene-dependent acoustic transfer functions (Luo et al., 2022); they map emitter-listener configurations to impulse responses rather than modeling intrinsic source emission. “NEF: Neural Edge Fields for 3D Parametric Curve Reconstruction from Multi-view Images” uses NEF for Neural Edge Field, a bounded continuous field of 3D edge probability trained through volume rendering of 2D edge maps (Ye et al., 2023). “Neural Brain Fields” presents a continuous spatiotemporal EEG voltage field, not a formally defined Neural Emission Field (Kedem et al., 20 Dec 2025).

Within the emitter-rendering sense, the defining property is not merely the use of a neural network. It is the absorption of the complete receiver-side direct-lighting integral into a coordinate-conditioned field. NEF consequently occupies a specific position in neural rendering: a portable, emitter-local neural representation that exchanges offline path tracing, model memory, and training cost for deterministic runtime illumination queries.