Notes on Learning Generative Models of 3D Structures

My notes from an overview of the Learning Generative Models of 3D Structures paper.

Christian Mills


December 9, 2021


I wanted to get an idea of where the research is at for using deep learning models to generate 3D models for applications in procedural generation tools and creating synthetic datasets. I came across a video going over the 2020 paper, Learning Generative Models of 3D Structures. Below are some notes I took while watching.


  • 3D Graphics are now critical to many industries
  • Huge cost in data capture and human labeling leads to lack of training data

Generative models

  • generative: \[ P(X) \ vs \ discriminative: P(Y|X) \]

  • Instead of learning to predict some attribute Y given an input X, the generative model learns the entire input distribution, enabling them to sample objects directly from X

  • Can be useful in simulating real-world environments and synthetically generating training data

Structure-Aware Representations

  • Scope: learned generative models of structured 3D content


  • Determined with data ↔︎ By hand or rules


  • 3D shapes and scenes that are decomposed into sub-structures ↔︎ a monolithic chunk of geometry


  • Express 3D shapes and scenes using abstractions that allow manipulation of their high-level structure
  • represent the geometry of the atomic structural elements
  • represent the structural patterns

Structure-Aware Representations

  • Representations of Part/Object Geometry
    • Voxel Grid
    • Point Cloud
    • Implicit Surface
      • A function that determines whether a point is inside or outside a surface
    • Triangle Mesh
  • Representations of Structure
    • Segmented geometry
      • Links a label to each part of the entity’s geometry
    • Part sets
      • an unordered set of atoms (pieces)
    • Relationship graphs
      • With edges between different parts of a scene or object
    • Hierarchies (trees)
    • Hierarchical Graphs
      • Combine relationship graphs and hierarchies
    • Deterministic Programs
      • Can be made to output any of the above representations
      • Beneficial for making patterns clear
      • Allows editing by users


Program synthesis

  • Constrain-based program synthesis
    • Used when only a few training examples are available
    • Tries to find the minimum cost program while satisfying some constraints

Classical Probabilistic Models

  • Probabilistic graphical models
    • Input Type:
      • Small dataset, not large enough to train a deep learning model
      • Fixed structure
    • Examples:
      • Factor graph
      • Bayesian network
      • Markov random field
  • Probabilistic grammars
    • Input Type:
      • Small dataset, not large enough to train a deep learning model
      • Dynamic, tree-like structure
    • Examples:
      • Context-free grammar (CFG)
        • Used in natural language processing
        • a start symbol
        • a set of terminals and non-terminals
        • a set of rules that map a non-terminal to another layout
        • generates a tree where the leaf nodes are terminals
      • Probabilistic CFG (PCFG)
        • Adds a probability of each rule

Deep Generative Models

  • Input Type:
    • Big dataset
  • Autoregressive models
    • Input Type:

      • Not globally-coherent
    • Iteratively consumes it’s output from one iteration as input for the next iteration

    • Weakness:

      • If one step drifts from the training data, it can cause subsequent output to diverge further
  • Deep latent variable models
    • Input Type:
      • Globally-coherent
    • Variational AutoEncoders (VAE)
    • Generative Adversarial Networks (GAN)
    • Code Idea:
      • Sample over a low dimensional latent space in a trained generator that maps latent vectors to actual 3D shapes which are hard to sample.
      • Use a global latent variable to control the generation
      • Trained with a reconstruction loss between the input and generated output
      • Often perform better than autoregressive models in terms of global coherence

Structure Type

  • Recurrent Neural Network
    • Data represented as a linear chain
  • Recursive Neural Network RvNN
    • Data represented as a tree
  • Graph Convolutional Network
    • Data represented as a graph
  • Neural Program Synthesis

## Application

  • Synthesize a plausible program that recreates an existing piece of 3D content

  • Recover shape-generating programs from an existing 3D shape

  • Learning Shape Abstractions by Assembling Volumetric Primitives (2017)

    • Learned to reconstruct 3D shapes with simple geometric primitives
    • Decompose shapes into primitives and used chamfer distance as a loss function

    Learning Shape Abstractions

    Learning Shape Abstractions by Assembling Volumetric Primitives

  • Learning to Infer and Execute 3D Shape Programs (2019)

    • Model can output a 3D shape program consisting of loops and other high level structures


    Learning to Infer and Execute 3D Shape Programs

  • Superquadrics Revisited: Learning 3D Shape Parsing beyond Cuboids

  • Perform visual program induction directly from 2D images

    • Liu et al. 2019 - Other Applications:
  • Part-based shape synthesis

  • Indoor scene synthesis