GAUDI: A Neural Architect for Immersive 3D Scene Generation
Anonymous Author(s)
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Abstract
We introduce GAUDI , a generative model capable of capturing the distribution ofcomplex and realistic 3D scenes that can be rendered immersively from a movingcamera.
We tackle this challenging problem with a scalable yet powerful approach,where we ﬁrst optimize a latent representation that disentangles radiance ﬁeldsand camera poses.
This latent representation is then used to learn a generativemodel that enables both unconditional and conditional generation of 3D scenes.
Our model generalizes previous works that focus on single objects by removingthe assumption that the camera pose distribution can be shared across samples.
We show that GAUDI obtains state-of-the-art performance in the unconditionalgenerative setting across multiple datasets and allows for conditional generation of3D scenes given conditioning variables like sparse image observations or text thatdescribes the scene.
Introduction
In order for learning systems to be able to understand and create 3D spaces, progress in generativemodels for 3D is sorely needed.
The quote "The creation continues incessantly through the mediaof man." is often attributed to Antoni Gaudí , who we pay homage to with our method’s name.
Inthis paper we ask the question: can creation continue through the media of learning machines?
Weare interested in generative models that can capture the distribution of 3D scenes and then renderviews from scenes sampled from the learned distribution.
Extensions of such generative models toconditional inference problems could have tremendous impact in a wide range of tasks in machinelearning and computer vision.
For example, one could sample plausible scene completions that areconsistent with an image observation, or a text description (see Fig.
1 for 3D scenes sampled from
GAUDI).
In addition, such models would be of great practical use in model-based reinforcementlearning and planning [12], SLAM [39], or 3D content creation.
Recent works on generative modeling for 3D objects or scenes [56, 5, 7] employ a Generative
Adversarial Network (GAN) where the generator explicitly encodes radiance ﬁelds — a parametricfunction that takes as input the coordinates of a point in 3D space and camera pose, and outputs adensity scalar and RGB value for that 3D point.
Images can be rendered from the radiance ﬁeldgenerated by the model by passing the queried 3D points through the volume rendering equationto project onto any 2D camera view.
While compelling on small or simple 3D datasets ( e . g .
singleobjects or a small number of indoor scenes), GANs suffer from training pathologies including modecollapse [54, 61] and are difﬁcult to train on data for which a canonical coordinate system does notexist, as is the case for 3D scenes [57].
In addition, one key difference between modeling distributionsof 3D objects vs. scenes is that when modeling objects, the distribution of valid camera poses doesnot depend on each object and is deﬁned per dataset ( i .
e .
typically as SO (3) ), which is not truefor scenes.
See Fig. 3(b) and note how the two scene layouts deﬁne different areas of navigablespace (different dark grey shaded areas) where valid camera poses can be placed, revealing a strong
[Figure]
dependency between scenes and their camera pose distributions. GAUDI captures this dependencyby modeling the joint distribution of scenes and camera poses.
In GAUDI, we map each trajectory ( i .
e .
a sequence of posed images from a 3D scene) into a latentrepresentation that encodes a radiance ﬁeld ( e .
g .
the 3D scene) and camera path in a completelydisentangled way.
We ﬁnd these latent representations by interpreting them as free parameters andformulating an optimization problem where the latent representation for each trajectory is optimizedvia a reconstruction objective.
This simple training process is scalable to thousands of trajectories.
Interpreting the latent representation of each trajectory as a free parameter also makes it simple tohandle a large and variable number of views for each trajectory rather than requiring a sophisticatedencoder architecture to pool across a large number of views.
After optimizing latent representationsfor an observed empirical distribution of trajectories, we learn a generative model over the set oflatent representations.
In the unconditional case, the model can sample radiance ﬁelds entirely fromthe prior distribution learned by the model, allowing it to synthesize scenes by interpolating within thelatent space.
In the conditional case, conditional variables available to the model at training time ( e .
g .images, text prompts, etc.) can be used to generate radiance ﬁelds consistent with those variables.
Our contributions can be summarized as:
• We scale 3D scene generation to thousands of indoor scenes containing hundreds of thousands of
images, without suffering from mode collapse or canonical orientation issues during training.
• We introduce a novel denoising optimization objective to ﬁnd latent representations that jointly model a radiance ﬁeld and the camera poses in a disentangled manner.• Our approach obtains state-of-the-art generation performance across
multiple datasets.•
Our approach allows for various generative setups: unconditional generation as well as conditionalon images or text.
Related Work
In recent years the ﬁeld has witnessed outstanding progress in generative modeling for the 2D imagedomain, with most approaches focusing either on adversarial [19, 20] or auto-regressive models[64, 42, 9].
More recently, score matching based approaches [16, 58] have gained popularity.
Inparticular, Denoising Diffusion Probabilistic Models (DDPMs) [15, 33, 48, 63] have emerged asstrong contenders to both adversarial and auto-regressive approaches.
In DDPMs, the goal is to learna step-by-step inversion of a ﬁxed diffusion Markov Chain that gradually transforms an empirical datadistribution to a ﬁxed posterior, which typically takes the form of an isotropic Gaussian distribution.
In parallel, the last couple of years have seen a revolution in how 3D data is represented within neuralnetworks.
By representing a 3D scene as a radiance ﬁeld, NeRF [29] introduces an approach tooptimize the weights of a MLP to represent the radiance of 3D points that fall inside the ﬁeld-of-viewof a given set of posed RGB images.
Given the radiance for a set of 3D points that lie on a rayshot from a given camera pose, NeRF [29] uses volumetric rendering to compute the color for thecorresponding pixel and optimizes the MLP weights via a reconstruction loss in image space.
A few attempts have also been made at incorporating a radiance ﬁeld representation within generativemodels.
Most approaches have focused on the problem of single objects with known canonicalorientations like faces or Shapenet objects with shared camera pose distributions across samples in adataset [56, 5, 34, 22, 4, 10, 70, 43].
Extending these approaches from single objects to completelyunconstrained 3D scenes is an unsolved problem.
One paper worth mentioning in this space is GSN[7], which breaks the radiance ﬁeld into a grid of local radiance ﬁelds that collectively represent ascene.
While this decomposition of radiance ﬁelds endows the model with high representationalcapacity, GSN still suffers from the standard training pathologies of GANs, like mode collapse [61],which are exacerbated by the fact that unconstrained 3D scenes do not have a canonical orientation.
As we show in our experiments (cf.
Sect. 4), these issues become prominent as the training set sizeincreases, impacting the capacity of the generative model to capture complex distributions.
Separately,a line of recent approaches have also studied the problem of learning generative models of sceneswithout employing radiance ﬁelds [36, 65, 47].
These works assume that the model has access toroom layouts and a database of object CAD models during training, simplifying the problem of scenegeneration to a selection of objects from the database and pose predictions for each object.
Finally, approaches that learn to predict a target view given a single (or multiple) source view andrelative pose transformation have been recently proposed [24, 69, 53, 8, 11].
The pure reconstructionobjective employed by these approaches forces them to learn a deterministic conditional function thatmaps a source image and a relative camera transformation to a target image.
The ﬁrst is that this scenecompletion problem is ill-posed ( e .
g .
given a single source view of a scene there are multiple targetcompletions that are equally likely).
Attempts at modeling the problem in a probabilistic manner havebeen proposed [49, 45].
However, these approaches suffer from inconsistency in predicted scenesbecause they do not explicitly model a 3D consistent representation like a radiance ﬁeld.
GAUDI
Our goal is to learn a generative model given an empirical distribution of trajectories over 3D scenes.
Let X
=
{ x i 2 { 0 ,...,n } } denote a collection of examples deﬁning an empirical distribution, where 100 each example x i is a trajectory.
Every trajectory x i is deﬁned as a variable length sequence ofcorresponding RGB, depth images and 6 DOF camera poses (see Fig. 3).
We decompose the task of learning a generative model in two stages.
First, we obtain a latentrepresentation z
=
[ z scene , z pose ] for each example x 2 X that represents the scene radiance ﬁeldand pose in separate disentangled vectors.
Second, given a set of latents Z = { z i 2 { 0 ,...,n } } we learnthe distribution p ( Z ) .
3.1 Optimizing latent representations for radiance ﬁelds and camera poses
We now turn to the task of ﬁnding a latent representation z 2 Z for each example x 2 X ( i .
e .
for eachtrajectory in the empirical distribution).
To obtain this latent representation we take an encoder-lessview and interpret z ’s as free parameters to be found via an optimization problem [2, 35].
To maplatents z to trajectories x , we design a network architecture ( i .
e .
a decoder) that disentangles cameraposes and radiance ﬁeld parameterization.
Our decoder architecture is composed of 3 networks(shown in Fig.
• The camera pose decoder network c (parameterized by ✓ c ), is responsible for predicting cameraposes ˆ T s 2 SE (3) at the normalized temporal position s 2 [  1 , 1] in the trajectory, conditioned onz pose which represents the camera poses for the whole trajectory.
To ensure that the output of c isa valid camera pose ( e . g .
an element of SE (3) )
, we output a 3 D vector representing a normalized quaternion q s for the orientation and a 3 D translation vector t s .
• The scene decoder network d (parameterized by ✓ d ), is responsible for predicting a conditioningvariable for the radiance ﬁeld network f .
This network takes as input a latent code that represents the scene z scene and predicts an axis-aligned tri-plane representation [37, 4] W 2 R 3 ⇥ S ⇥ S ⇥ F .
Whichcorrespond to 3 feature maps [ W xy , W xz , W yz ] of spatial dimension S ⇥ S and F channels, onefor each axis aligned plane: xy , xz and yz .•
The radiance ﬁeld decoder network f (parameterized by ✓ f ), is tasked with reconstructing imagelevel targets using the volumetric rendering equation in Eq.
The input to f is p 2 R 3 and thetri-plane representation W =
[ W xy , W xz , W yz ] (we do not condition on the camera orientation to [Table] [Figure] improve consistency [10]).
Given a 3 D point p
=
[ i, j, k ] for which radiance is to be predicted, weorthogonally project p into each plane in W and perform bi-linear sampling.
We concatenate the 3bi-linearly sampled vectors into w xyz =
[ W xy ( i, j ) , W xz ( j, k ) , W yz ( i, k )] 2 R 3 F , which is usedto condition the radiance ﬁeld function f .
We implement f as a MLP that outputs a density value and a signal a .
To predict the value v of a pixel, the volumetric rendering equation is used (cf. Eq.
1)where a 3D point is expressed as ray direction r (corresponding with the pixel location) at particulardepth u .
[Equation]
We formulate a reconstruction objective to jointly optimize for ✓ d , ✓ c , ✓ f and { z } i = { 0 ,...,n } , shown in 134 Eq. 2.
Note that while latents z are optimized for each example x independently, the parameters of thenetworks ✓ d , ✓ c , ✓ f are amortized across all examples x 2 X .
As opposed to previous auto-decodingapproaches [2, 35], each latent z is perturbed during training with additive noise that is proportionalto the empirical standard deviation across all latents, z = z +  N (0 , std( Z )) , inducing a contractiverepresentation [46].
In this setting,  controls the trade-off between the entropy of the distributionof latents z 2 Z and the reconstruction quality. With  =
the distribution of z ’s becomes a set ofindicator functions ( i . e . similar as one would get from a vanilla auto-encoder). For large  > 0 thestructure in distribution of z ’s is destroyed, as latents are perturbed with large magnitudes of noise.
We use a small  > 0 value to enforce a latent space in which interpolated samples (or samples thatcontain small deviations from the empirical distribution, as the ones that one might get from samplinga subsequent generative model) are included in the support of the decoder function, sacriﬁcing asmall cost in reconstruction ﬁdelity.
[Equation]
We optimize parameters ✓ d , ✓ f , ✓ c and latents z 2 Z with two different losses.
The ﬁrst loss function
L scene measures the reconstruction between the radiance ﬁeld encoded in z scene and the images inthe trajectory x im s (where s denotes the normalized temporal position of the frame in the trajectory),given ground-truth camera poses T s required for rendering.
We use an l 2 loss for RGB and l 1 fordepth 1 .
The second loss function L pose measures the camera pose reconstruction error betweenthe poses ˆ T s encoded in z pose and the ground-truth poses.
We employ an l 2 loss on translation andl 1 loss for the normalized quaternion part of the camera pose.
Although theoretically normalizedquaternions are not necessarily unique ( e .
g .
q and  q ) we do not observe any issues empiricallyduring training.
3.2 Prior Learning
Given a set of latents z 2 Z resulting from minimizing the objective in Eq.
2, our goal is to learn agenerative model p ( Z ) that captures their distribution ( i .
e .
after minimizing the objective in Eq.
2we interpret z 2 Z as examples from an empirical distribution in latent space).
In order to modelp ( Z ) we employ a Denoising Diffusion Probabilistic Model (DDPM)
[15], a recent score-matching[16] based model that learns to reverse a diffusion Markov Chain with a large but ﬁnite number oftimesteps.
In DDPMs [15] it is shown that this reverse process is equivalent to learning a sequence ofdenoising auto-encoders with tied weights.
The supervised denoising objective in DDPMs makeslearning p ( Z ) simple and scalable.
This allows us to learn a powerful generative model that enablesboth unconditional and conditional generation of 3D scenes.
For training our prior p ✓ p ( Z ) we takethe objective function in [15] deﬁned in Eq.
In Eq.
3 t denotes the timestep, ✏ ⇠ N (0 , I ) isthe noise and ¯ ↵ t is a noise magnitude parameter with a ﬁxed scheduling.
Finally, ✏ ✓ p denotes thedenoising model.
[Equation]
At inference time, we sample z ⇠ p ✓ p ( Z ) by following the inference process in DDPMs.
We start bysampling z T ⇠ N (0 , I ) and iteratively apply ✏ ✓ p to gradually denoise z T , thus reversing the diffusion Markov Chain to obtain z 0 .
We then feed z 0 as input to the decoder architecture (cf.
Fig.
2) andreconstruct a radiance ﬁeld and a camera path.
If the goal is to learn a conditional distribution of the latents p ( Z | Y ) , given paired data { z 2 Z, y 2 173 Y } , the denoising model ✏ ✓ is augmented with a conditioning variable y , resulting in ✏ ✓ p ( z , t, y ) ,implementation details about how the conditioning variable is used in the denoising architecture canbe found in the appendix C.
Experiments
In this section we show the applicability of GAUDI to multiple problems.
First, we evaluatereconstruction quality and performance of the reconstruction stage.
Then, we evaluate the performanceof our model in generative tasks including unconditional and conditional inference, in which radianceﬁelds are generated from conditioning variables corresponding to images or text prompts.
Fullexperimental settings and details can be found in the appendix B.
4.1 Data
We report results on 4 datasets: Vizdoom [21], Replica [60], VLN-CE [23] and ARKit Scenes [1],which vary in number of scenes and complexity (see Fig.
3 and Tab. 1).
Vizdoom [21]: Vizdoom is a synthetic simulated environment with simple texture and geometry.
Weuse the data provided by [7] to train our model.
It is the simplest dataset in terms of number of scenesand trajectories, as well as texture, serving as a test bed to examine GAUDI in the simplest setting.
Replica [60]: Replica is a dataset comprised of 18 realistic scenes from which trajectories arerendered via Habitat [55].
We used the data provided by [7] to train our model.
VLN-CE [23]: VLN-CE is a dataset originally designed for vision and language navigation incontinuous environments.
This dataset is composed of 3 .
6 K trajectories of an agent navigatingbetween two points in a 3D scene from the Matterport 3D dataset [6].
We render observations via
Habitat [55].
Notably, this dataset contains also textual descriptions of the trajectories taken by anagent.
In Sect.
4.5 we train GAUDI in a conditional manner to generate 3D scenes given a description.
ARKitScenes [1]: ARKitScenes is a dataset of scans of indoor spaces.
This dataset contains morethan 5 K scans of about 1 .
6 K different indoor spaces.
As opposed to the previous datasets where
RGB, depth and camera poses are obtained via rendering in a simulation ( i .
e .
either Vizdoom [21] or
Habitat [55]) , ARKitScenes provides raw RGB and depth of the scans and camera poses estimatedusing ARKit SLAM.
In addition, whereas trajectories from the previous datasets are point-to-point,as typically done in navigation, the camera trajectories for ARKitScenes resembles a natural scan aof full indoor space.
In our experiments we use a subset of 1 K scans from ARKitScenes to train ourmodels.
[Figure] [Figure]
We ﬁrst validate the hypothesis that the optimization problem described in Eq.
2 can ﬁnd latent codesz that are able reconstruct the trajectories in the empirical distribution in a satisfactory way.
In Tab.
1we report reconstruction performance of our model across all datasets.
Fig.
4 shows reconstructionsof random trajectories for each dataset.
For all our experiments we set the dimension of z scene andz pose to 2048 and  = 0 .
unless otherwise stated.
During training, we normalize camera poses foreach trajectory so that the middle frame in a trajectory becomes the origin of the coordinate system.
See appendix E for ablation experiments.
[Figure]
4.3 Interpolation
In addition, to evaluate the structure of the latent representation obtained from minimizing theoptimization problem in Eq.
2, we show interpolation results between pairs of latents ( z i , z j ) in
Fig.
To render images while interpolating the scene we place a ﬁxed camera at the origin of thecoordinate system.
We observe a smooth transition of scenes in both geometry (walls, ceilings) andtexture (stairs, carpets).
More visualizations are included in the appendix G.
4.4 Unconditional generative modeling
Given latent representations z 2 Z that can reconstruct samples x 2 X with high accuracy asshown in Sect.
4.2, we now evaluate the capacity of the prior p ✓ p ( Z ) to capture the empiricaldistribution x 2 X by learning the distribution of latents
z
i 2 Z . To do so we sample z ⇠ p ✓ p ( Z ) 221 by following the inference process in DDPMs, and then feed z through the decoder network, whichresults in trajectories of RGB images that are then used for evaluation.
We compare our approach
[Table]
/1qza27M6Bl4hWkBgWa/eqXP5AkjakwhGOte56bmCDDyjDC6bTip5ommIzxkPYsFTimOshmmafoxCoDFEllnzBopv7eyHCs9SQO7WSeUS96ufif10tNdBVkTCSpoYLMD0UpR0aivAA0YIoSwyeWYKKYzYrICCtMjK2pYkvwFr+8TNpnde+ifn53XmtcF3WU4QiO4RQ8uIQG3EITWkAggWd4hTcndV6cd+djPlpyip1D+APn8weGwJIE</latexit>
z j with the following baselines: GRAF [56], ⇡ -GAN [5] and GSN [7], where all models have accessto ground-truth depth information during training.
We sample 5 k images from predicted and targetdistributions for each model and dataset and report both FID [14] and SwAV-FID [31] scores.
We report quantitative results in Tab. 2, where we can see that GAUDI obtains state-of-the-artperformance across all datasets and metrics.
We attribute this performance improvement to the factthat GAUDI learns disentangled yet corresponding latents for radiance ﬁelds and camera poses, whichis key when modeling scenes (see ablations in the appendix E).
We note that to obtain these greatempirical results GAUDI needs to simultaneously ﬁnd latents with high reconstruction ﬁdelity whilealso efﬁciently learning their distribution.
[Figure]
[Table]
In Fig.
6 we show samples from the unconditional distribution learnt by GAUDI for different datasets.
We observe that GAUDI is able to generate diverse and realistic 3D scenes from the empiricaldistribution which can be rendered from the sampled camera poses.
4.5 Conditional Generative Modeling
GAUDI can also tackle conditional generative problems of the form p ( Z | Y ) , where a conditioningvariable y 2 Y is given to condition p ( Z ) .
For a given conditional inference problem we assume theexistence of paired data [42, 9, 41]. As an example, for training a text-conditional model we assumethe existence of pairs { z i , y i } , where z i is a latent scene representation and y i is its correspondingtext prompt.
In this section we show both quantitative and qualitative results for conditional inferenceproblems.
The ﬁrst conditioning variable we consider are textual descriptions of trajectories.
Second,we consider a model where randomly sampled RGB images in a trajectory act as conditioning.
Finally,we use a categorical variable that indicates the 3D environment ( i .
e .
the particular indoor space) fromwhich each trajectory was obtained.
Tab.
3 shows quantitative results for the different conditionalinference problems.
Details on the implementation of the conditional DDPM are given in Sect.
D
[Table]
4.5.1 Text Conditioning
We tackle the challenging task of training a text conditional model for 3D scene generation.
Weuse the navigation text descriptions provided in VLN-CE [23] to condition our model.
These textdescriptions contain high level information about the scene as well as the navigation path ( i .
e . "
Walkout of the bedroom and into the living room" , "Exit the room through the swinging doors andthen enter the bedroom" ).
We employ a pre-trained RoBERTa-base [26] text encoder and use itsintermediate representation to condition the diffusion model.
Fig.
7 shows qualitative results of
GAUDI for this task.
To the best of our knowledge, this is the ﬁrst model that allows for conditional3D scene generation from text in an amortized manner ( i .
e .
without distilling CLIP [40] through acostly optimization problem [17, 28]).
[Figure]
4.5.2 Image Conditioning
We now analyze whether GAUDI is able to pick up information from the RGB images to predict adistribution over Z .
In this experiment we randomly pick images in a trajectory x 2 X and use it as aconditioning variable y .
For this experiment we use trajectories in the VLN-CE dataset [23].
Duringeach training iteration we sample a random image for each trajectory x and use it as a conditioningvariable.
We employ a pre-trained ResNet-18 [13] as an image encoder.
During inference, theresulting conditional GAUDI model is able to sample radiance ﬁelds where the given image isobserved from a stochastic viewpoint.
In Fig.
8 we show samples from the model conditioned ondifferent RGB images. [Figure]
4.5.3 Categorical Conditioning
Finally, we analyze how GAUDI performs when conditioned on a categorical variable that indicates the underlying 3D indoor environment in which each trajectory was recorded.
We performexperiments in the VLN-CE [23] dataset, where we employ a trainable embedding layer to learn a representation for categorical variables indicating each environment.
We compare the per-environment
FID score of conditional model with its unconditional counterpart.
This per-enviroment FID scoreis computed only on real images of the same indoor environment that the model is conditioned on.
Our hypothesis is that if the model efﬁciently captures the information in the conditioning variableit should capture the environment speciﬁc distribution better than its unconditional counterparttrained on the same data.
In Tab. 3 the last column shows difference ( e . g .
the  ) on the averageper-environment FID score between the conditional and unconditional model on VLN-CE dataset.
We observe that the conditional model consistently obtains a better FID score than the unconditionalmodel across all indoor environments, resulting in a sharp reduction of average FID and SwAV-FIDscores.
In addition, in Fig.
9 we show samples from the model conditioned on a given categoricalvariable.
Conclusion
We have introduced GAUDI, a generative model that captures distributions of complex and realistic3D scenes.
GAUDI uses a scalable two-stage approach which ﬁrst involves learning a latent representation that disentangles radiance ﬁelds and camera poses.
The distribution of disentangled latentrepresentations is then modeled with a powerful prior.
Our model obtains state-of-the-art performancewhen compared with recent baselines across
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