DiffusioNeRF: Diffusion-Enhanced NeRF

• DiffusioNeRF is a framework that combines denoising diffusion models with Neural Radiance Fields to overcome ambiguities in 3D scene reconstruction under limited supervision.
• It employs both patch-based and grid-based diffusion techniques to regularize the training process, guiding the NeRF optimization toward physically plausible and consistent solutions.
• Empirical results on datasets like LLFF, DTU, and ShapeNet demonstrate improved novel view synthesis, accurate depth estimation, and diverse scene generation.

DiffusioNeRF refers to a class of methods that integrate denoising diffusion probabilistic models (DDMs) with Neural Radiance Fields (NeRFs) for synthesizing, regularizing, or generating novel 3D scene representations. These approaches impose learned, data-driven priors on NeRF training or reconstruction and thus address key limitations of conventional NeRFs, especially in ambiguous or low-supervision settings. Distinct from approaches such as DiffRF that synthesize 3D radiance fields directly via diffusion, DiffusioNeRF methods primarily employ diffusion models as statistical regularizers or priors, leveraging the gradient of the log-likelihood of photometric and geometric patches to bias NeRF representations towards physically plausible and visually consistent solutions (Wynn et al., 2023, Yang et al., 2023).

1. Motivation and Foundations

NeRFs learn continuous volumetric representations of 3D scenes by minimizing the discrepancy between rendered and observed images, typically using a photometric reconstruction loss. Despite their success in novel view synthesis, NeRFs are fundamentally under-constrained, especially when trained on sparsely observed scenes. Ambiguities in object geometry and color often manifest as artifacts, such as "floaters" or incorrect depth structures. Hand-crafted regularizers have limited capacity to encode the rich statistical structure of real-world scenes.

DiffusioNeRF addresses these limitations by introducing learned priors based on denoising diffusion models. DDMs are generative models that, when trained on collections of data (e.g., RGBD image patches or structured NeRF grids), learn to approximate the gradient of the data distribution’s log-probability (i.e., the score function). This key property enables the deployment of such priors during NeRF training as differentiable regularizers, steering the optimization toward realistic scenes even under insufficient supervision (Wynn et al., 2023).

2. Integration of Diffusion Models and NeRFs

The integration strategy employed in DiffusioNeRF consists of the following core components:

• Training the Diffusion Model: A DDM, such as a 3D U-Net, is trained on RGBD patches (small spatial crops combining color and depth) from a database of rendered images and depth maps (e.g., Hypersim). The diffusion process corrupts patches via Gaussian noise, and the DDM is trained to predict the added noise at varying diffusion steps. By the established relation $$\epsilon_\theta(x_\tau, \tau) \propto -\nabla_x \log p(x)$$, the trained model provides an estimate of the gradient of log-likelihood with respect to an input patch (Wynn et al., 2023).
• Regularization During NeRF Training: As the NeRF is optimized on target scene data, random RGBD patches are rendered from the current field estimate. These patches are input to the DDM, and the predicted gradients are backpropagated through the photometric and geometric fields of the NeRF. The total training gradient is a composite,

$$\nabla\mathcal{L} = \nabla \mathcal{L}_{\text{photo}} + \lambda_{\text{fg}}\nabla \mathcal{L}_{\text{fg}} + \lambda_{\text{fr}}\nabla \mathcal{L}_{\text{fr}} + \lambda_{\text{dist}}\nabla\mathcal{L}_{\text{dist}} - \lambda_{\text{DDM}}\epsilon_\theta,$$

where the DDM term attracts the learned radiance fields towards high-probability RGBD configurations (Wynn et al., 2023).

• Regularization via Structured Fields: An alternative approach encodes NeRFs as structured feature grids—"regularized ReLU-fields"—which are denoised via 3D convolutional architectures in the diffusion model (Yang et al., 2023). This facilitates generative modeling in a space amenable to both learning scene distributions and efficient denoising.

3. Methodological Details

DiffusioNeRF: Patch-Based Diffusion Prior

• Patch Construction: NeRF is equipped with fast rendering backends (e.g., Instant NGP and tiny-cuda-nn), enabling efficient extraction of random $48\times48$ RGBD patches from current field estimates during training.
• Supervision Schedule: Early in NeRF training, a substantial portion of the RGB patches input to the DDM are sampled from ground-truth images. This "hinting" helps stabilize the learned prior application. As training proceeds, the DDM is presented with increasingly accurate predictions from the evolving NeRF (Wynn et al., 2023). The noise parameter $\tau$ is decreased from 0.1 to 0 as reconstructions improve, tuning the regularization strength.

Diffusion Prior: Grid-Based Generative Modeling

• Regularized Grids: NeRF scenes are encoded as 3D feature grids, rather than as MLP weights, using a combination of photometric loss, density sparsity, and color constancy constraints. This reduces degenerate solutions and improves consistency for the diffusion generative model (Yang et al., 2023).
• 3D Diffusion Model: The diffusion model operates on these tensors, learning the distribution $p(V)$ via the standard DDPM framework, with noise schedules $(\alpha_t, \sigma_t)$ and a learning procedure governed by

$$\mathcal{L}_T = \frac{T}{2}\mathbb{E}_{(V, z, t)}[w(t)\|\epsilon - \hat{\epsilon}_\theta(V,t)\|^2].$$

Sampling proceeds by iteratively denoising from pure noise toward a NeRF grid plausibly representative of the training data.

Conditional Generation with Diffusion Guidance

A major strength of the diffusion approach is its flexibility for conditional generation. Bayes' rule is employed to combine a generative prior with observed evidence (such as a single input image):

$$p_\theta(V_{s(i)}|V_{t(i)},y) \propto p_\theta(y|V_{s(i)}) \cdot p_\theta(V_{s(i)}|V_{t(i)}).$$

The gradient of $\log p_\theta(y|V)$ with respect to $V$ can be computed via the photometric rendering loss and used for test-time latent guidance. This facilitates applications such as image-to-3D reconstruction or inpainting (Yang et al., 2023).

4. Empirical Results and Benchmark Evaluations

Evaluations of DiffusioNeRF approaches span key datasets:

• LLFF (Limited Views): Under sparse observation (3, 6, or 9 views), the addition of the DDM prior results in improved novel view synthesis quality and more plausible geometry compared to hand-crafted or no regularization. While some metrics of photometric quality (PSNR, SSIM, LPIPS) are achieved by geometric baselines, their depth maps are often implausible; by contrast, DiffusioNeRF yields smoother and physically realistic surfaces (Wynn et al., 2023).
• DTU (Object-Centric Reconstruction): DiffusioNeRF exhibits lower Chamfer L1 distance relative to baseline NeRF methods, supporting more accurate geometry estimation even in ambiguous spatial configurations or scenes with low texture.
• ShapeNet (Category-Level Generation): When trained on regularized NeRF grids, the diffusion priors yield high-fidelity samples with greater shape and color diversity, confirming the importance of regularization at the grid encoding stage for generative quality (Yang et al., 2023).

Table: Comparative Outcomes

Dataset	Main Baseline	Regularization Effect
LLFF	Geometric	Smoother, more plausible geometry with DDM prior
DTU	NeRF variants	Lower Chamfer-L1 distance, improved reconstruction
ShapeNet	ReLU-fields	Greater diversity and realism in NeRF samples

5. Applications and Implications

DiffusioNeRF frameworks enable several advanced applications that conventional NeRFs or 3D GANs find challenging:

• Few-View and Single-View Reconstruction: Regularization via a learned diffusion prior enables NeRF to infer plausible scene geometry and appearance with little supervision, addressing a longstanding limitation of neural scene representation (Wynn et al., 2023, Yang et al., 2023).
• Conditional Generation: Classical approaches struggle with inpainting or completion in 3D. The diffusion-based prior allows masked field completion, text-conditioned sampling (if extended with CLIP or similar), and other forms of guided or conditional NeRF synthesis (Müller et al., 2022, Yang et al., 2023).
• Generative Modeling of Scene Classes: A diffusion prior over entire scene categories supports 3D shape and appearance sampling directly in the NeRF space, facilitating the randomized creation of plausible novel scenes.

A plausible implication is the extension of DDM-based regularization frameworks to monocular and self-supervised reconstruction tasks, or direct regularization of 3D voxel fields in other domains.

6. Limitations and Future Directions

Areas for advancement include:

• Objective Integration: Current methods often combine the DDM gradient and NeRF loss heuristically (with schedule and weight parameters, e.g., $\tau$ and $\lambda_{\text{DDM}}$). A more rigorous joint objective, potentially derived from probabilistic or variational principles, remains an open challenge (Wynn et al., 2023).
• Guidance Optimization: Conditional diffusion guidance can be susceptible to local minima, particularly when shape cues are ambiguous or inconsistent across conditioning signals (Yang et al., 2023).
• Scalability: Further work may focus on scaling up grid resolutions, accelerating sampling procedures, and integrating multimodal conditioning signals.

The unification of DDMs as flexible, differentiable priors for gradient descent in 3D representation learning represents a promising direction for robust and versatile scene understanding (Wynn et al., 2023, Yang et al., 2023).

7. Relation to Related Approaches

DiffusioNeRF is distinct from methods such as DiffRF (Müller et al., 2022), which directly synthesizes explicit volumetric radiance fields via diffusion, bypassing photometric renderings. DiffusioNeRF and related score-based regularization frameworks instead act as learned statistical priors, shaping the solution space explored by an underlying optimization or conditional inference procedure.

The methodological comparison between 3D GANs, patch-based score regularization, and grid-based generative NeRF diffusion models elucidates a spectrum of design tradeoffs between generative flexibility, sample fidelity, and inference-time versatility.