What Is Latent Space? The Hidden Engine Behind Modern AI
- Muiz As-Siddeeqi
- 7 days ago
- 28 min read
The Invisible Force Shaping Every AI Image, Song, and Word You Experience
Every time you ask ChatGPT a question, generate an image with DALL-E, or receive a Spotify recommendation, you're witnessing latent space at work. This mathematical concept, invisible to users but essential to engineers, has become the foundation of modern artificial intelligence. In 2024 alone, AI systems leveraging latent space representations processed over 4 billion prompts daily across major platforms (Founders Forum Group, 2025). Yet most people have never heard of it.
Latent space is the compressed, abstract dimension where AI models store the essence of data—stripping away noise and keeping only what matters. It's why a 512×512 pixel image can be represented in just 4,096 numbers instead of 786,432, and why your music app can understand that you like both jazz and electronic music without storing every song you've ever played.
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TL;DR: Key Takeaways
Latent space is a compressed representation that captures essential features of data while discarding redundant information
Modern AI systems use latent spaces to reduce computational requirements by 48 to 256 times compared to raw data processing
The global generative AI market, heavily dependent on latent space techniques, reached $16.87 billion in 2024 and will grow to $109 billion by 2030 (Grand View Research, 2024)
Real-world applications include Stable Diffusion (image generation), Spotify's FS-VAE (music recommendations), and OpenAI's GPT embeddings (language understanding)
Companies save millions in infrastructure costs by processing data in latent space rather than pixel or token space
Dimensionality reduction from thousands or millions of dimensions to just hundreds enables real-time AI responses
Latent space is a compressed, lower-dimensional representation of data that machine learning models use to capture essential patterns and relationships. Instead of processing raw pixels or text, AI systems map data into latent space where similar items cluster together, enabling efficient generation, classification, and manipulation of complex information like images, audio, and language.
Table of Contents
Background & The Evolution of Latent Space
The concept of latent space didn't emerge overnight. Its roots trace back to classical statistical methods developed decades before modern deep learning.
Early Foundations: PCA and LDA
In the 1930s, Harold Hotelling introduced Principal Component Analysis (PCA), a technique for reducing data dimensionality while preserving variance (Metaschool, 2024). PCA became the first widely-used method for creating lower-dimensional representations of complex data. Linear Discriminant Analysis (LDA) followed, adding supervised learning to the mix by finding dimensions that best separated different classes.
These methods laid the groundwork, but they had a critical limitation: they could only capture linear relationships. Real-world data—images, sounds, language—contains complex, non-linear patterns that simple linear transformations couldn't capture.
The Neural Network Revolution
The breakthrough came with autoencoders, neural networks that learn to compress and reconstruct data. Unlike PCA's fixed linear transformation, autoencoders discovered non-linear relationships through training on massive datasets. The encoder squeezes data into a latent representation, and the decoder reconstructs it.
In 2013, Diederik Kingma and Max Welling published their seminal paper introducing Variational Autoencoders (VAEs), which added probabilistic structure to latent spaces (V7 Labs, 2024). This innovation enabled not just compression but generation of entirely new, realistic data points.
The Modern Era: VQ-VAE and Latent Diffusion
The 2017 introduction of VQ-VAE (Vector Quantized Variational Autoencoder) by van den Oord marked another leap. By 2018, this evolved into VQ-GAN, which combined adversarial learning with vector quantization (Sander Dieleman, 2025). VQ-GAN increased compression ratios from 4× to 16×—meaning a 512×512 image could be represented in just 32×32 latent codes—while maintaining sharp, realistic reconstructions.
This technology became the foundation for Stable Diffusion, released in 2022. Sander Dieleman, a senior research scientist, stated that VQ-GAN "probably the main reason why GANs deserved to win the Test of Time award at NeurIPS 2024" (Sander Dieleman, 2025).
Today, latent space techniques power the $16.87 billion generative AI market (Grand View Research, 2024), with applications spanning image generation, language modeling, drug discovery, and music composition.
What Exactly Is Latent Space?
Latent space is a compressed, abstract representation of data that preserves only the essential features needed to understand the data's underlying structure.
Think of it like this: When you describe a car to someone, you don't recite every pixel of its appearance. You mention key features—color, size, shape, brand. Latent space works similarly. It stores the "car-ness" in a few hundred numbers instead of millions of pixels.
The Core Principles
Dimensionality Reduction: Latent space dramatically reduces data size. IBM's documentation notes that a latent space representation "typically entails some degree of dimensionality reduction: the compression of high-dimensional data down to a lower-dimensional space that omits irrelevant or redundant information" (IBM, 2024).
Semantic Organization: Similar items cluster together in latent space. Images of cats occupy one region, dogs another. This organization emerges naturally from training, not from explicit programming.
Continuous Structure: Unlike raw data with discrete jumps, latent spaces are smooth and continuous. You can interpolate between two points and get meaningful intermediate representations. Move gradually from a cat's latent representation to a dog's, and you'll pass through cat-dog hybrids.
A Real Example: Image Compression
Stable Diffusion compresses a 512×512×3 image (786,432 numbers) into a 64×64×4 latent representation (16,384 numbers)—48 times smaller (Stable Diffusion Art, 2024). This compression happens through a Variational Autoencoder (VAE) that learned, through training on billions of images, which features matter and which don't.
The compressed latent keeps structural information—edges, shapes, textures—while discarding pixel-level noise. When you generate an image, the diffusion process operates entirely in this tiny latent space, making generation feasible on consumer hardware.
How Latent Space Works Technically
Creating and using latent space involves three main components: an encoder, the latent representation itself, and a decoder.
The Encoder: Data Compression
The encoder is a neural network that transforms high-dimensional input data into a low-dimensional latent vector. For images, this might be a series of convolutional layers that progressively reduce spatial dimensions while increasing feature channels.
In Stable Diffusion's VAE, the encoder converts a 512×512×3 RGB image into a 64×64×4 latent tensor (NVIDIA NeMo, 2024). The encoder learns through training which patterns matter: edges, textures, object boundaries, color distributions.
The Latent Representation
The latent representation is a vector or tensor of numbers encoding the compressed information. These numbers don't directly correspond to observable features like "blueness" or "roundness." Instead, they encode abstract, learned features that the neural network discovered during training.
In language models like GPT-3, embeddings have 12,288 dimensions (Dugas, 2024). Each dimension captures some aspect of word meaning, though researchers still debate exactly what each dimension represents.
The Decoder: Reconstruction
The decoder reverses the encoding process, transforming latent vectors back into observable data. In VAEs, the decoder learns to reconstruct inputs as faithfully as possible from their compressed latent representations.
Sander Dieleman notes that in Stable Diffusion, "latent representations tend to preserve a lot of signal structure... They basically look like noisy, low-resolution images with distorted colors" (Sander Dieleman, 2025). This means the latent space isn't truly abstract—it retains recognizable structure.
Training Process
Autoencoders train by minimizing reconstruction error: the difference between the original input and the decoder's output. VAEs add a second loss term—KL divergence—that encourages the latent space to follow a smooth, continuous distribution (typically a normal distribution).
This dual objective creates latent spaces that are both accurate (low reconstruction error) and generative (smooth enough to sample new points from).
The Mathematics Made Simple
While the full mathematics involves complex calculus and probability theory, the core concepts are straightforward.
Vector Representation
Every data point becomes a vector (a list of numbers) in latent space. A 200-dimensional latent vector for an image might look like:
[0.43, -1.2, 0.89, 2.1, ..., -0.65]Each number represents a learned feature. Similar images have similar vectors.
Distance and Similarity
Distance between vectors indicates similarity. Two vectors with a small Euclidean distance represent similar concepts:
Distance = √[(x₁-y₁)² + (x₂-y₂)² + ... + (xₙ-yₙ)²]OpenAI's text-embedding-3-small model uses 1,536-dimensional vectors, where cosine distance measures semantic similarity (OpenAI, 2024). Sentences with similar meanings have vectors pointing in similar directions.
Interpolation
You can create intermediate points by averaging vectors:
Intermediate = 0.5 × Vector_A + 0.5 × Vector_BThis linear interpolation in latent space produces smooth transitions. Generate an image from a cat's latent vector, another from a dog's, then generate from their average—you get a plausible cat-dog blend.
Compression Ratio
Compression ratio measures efficiency:
Compression Ratio = (Input Dimensions) / (Latent Dimensions)Stable Diffusion achieves a 48× compression ratio (786,432 pixels → 16,384 latent values) (Stable Diffusion Art, 2024). DALL-E compresses 256×256 images into 32×32 grids (1,024 tokens) for an 8× spatial compression (OpenAI, 2021).
Real-World Applications
Latent space powers applications across industries, from entertainment to healthcare.
Image Generation
Stable Diffusion operates entirely in latent space, making it possible to generate 512×512 images on consumer GPUs with 16GB memory (Stable Diffusion Art, 2024). All diffusion steps happen in the compressed 64×64×4 space, then the VAE decoder upsamples to full resolution.
DALL-E uses a discrete VAE that compresses 256×256×3 images into 32×32 grids of 1,024 tokens from an 8,192-token vocabulary (GitHub - simonsanvil, 2024). This compression enables a 12-billion-parameter transformer to generate images autoregressively.
Music Recommendation
Spotify deployed FS-VAE (Fast and Slow Variational Autoencoder) in 2022 to model user preferences (Spotify Research, 2022). The model separates slow-moving features (general taste) from fast-moving features (momentary mood), both represented in latent space. This approach "showed clear improvements over the prediction task compared to state-of-the-art approaches" on next-track prediction (Spotify Research, 2022).
Language Understanding
OpenAI's embedding models transform text into semantic latent representations. The text-embedding-3-small model creates 1,536-dimensional vectors, while text-embedding-3-large uses 3,072 dimensions (OpenAI, 2024). These embeddings power ChatGPT's knowledge retrieval and semantic search features.
On multilingual retrieval benchmarks (MIRACL), OpenAI's new embeddings improved from 31.4% to 44.0% average score compared to their previous generation (OpenAI, 2024).
MIT researchers use VAEs for molecular design, encoding chemical structures into latent space, then sampling new points to discover novel drug candidates (Medium, 2023). The latent representation captures chemical properties like solubility and binding affinity.
Video Compression
CV-VAE (Compatible Video VAE) extends latent space techniques to video, achieving 4× temporal compression on top of 8× spatial compression (ArXiv, 2024). This enables generation of longer videos within the same computational budget.
Case Study: Stable Diffusion's Latent Compression
Company: Stability AI
Technology: Latent Diffusion Model (LDM)
Launch Date: August 2022
Impact: Democratized AI image generation by making it accessible on consumer hardware
The Challenge
Traditional diffusion models operated in pixel space, requiring massive computational resources. Generating a single 512×512 image took minutes on high-end GPUs and consumed gigabytes of memory.
The Solution
Stability AI, building on research from CompVis at LMU Munich, implemented latent diffusion. The system consists of three parts (Wikipedia, 2025):
VAE Encoder: Compresses 512×512×3 images (786,432 values) into 64×64×4 latent tensors (16,384 values)
U-Net: Performs diffusion/denoising in latent space
VAE Decoder: Upsamples latent representations back to full-resolution images
The Results
This 48× compression made Stable Diffusion runnable on consumer GPUs. Users could generate images on $500 graphics cards in their homes, not just on $100,000 cloud infrastructure.
By September 2022, Stable Diffusion was publicly released without API costs. Within months, users generated millions of images daily. The model's 860 million parameters in the U-Net and 123 million in the text encoder made it "relatively lightweight by 2022 standards" (Wikipedia, 2025).
Measurable Impact
Stable Diffusion processes operate 48 times faster than pixel-space alternatives
Memory requirements reduced from 48GB to 1GB per batch
Generated over 4 million images per day by late 2022 (OpenAI API announcement, 2024)
Enabled countless derivative applications: image editing, style transfer, inpainting
Key Insight
The compression ratio directly determines feasibility. Without latent space, consumer-grade AI art wouldn't exist. As noted in the Stable Diffusion documentation: "That's why it's a lot faster" (Stable Diffusion Art, 2024).
Case Study: Spotify's Music Recommendation Engine
Company: Spotify
Technology: FS-VAE (Fast and Slow Variational Autoencoder)
Publication Date: February 2022
Dataset: 28 days of listening data from millions of users
The Challenge
Music preferences are complex. Users have stable, long-term tastes (favorite genres, artists) and volatile, short-term moods (workout energy, bedtime calm). Traditional collaborative filtering struggled to balance these timescales.
The Solution
Spotify developed FS-VAE, which processes two types of features in separate components (Spotify Research, 2022):
Slow-moving features (general preferences): processed by a non-sequential encoder
Fast-moving features (recent listening): processed by a sequential LSTM encoder
Both encode into a shared latent space representing the user's current state. The decoder predicts the next track from this unified representation.
The Technical Details
The model learns an 80-dimensional track representation space. Each user's state is encoded as a latent vector combining stable preferences and recent context. The VAE architecture ensures this latent space is smooth and continuous.
Researchers compared performance using two metrics:
Norm-2 distance between predicted and actual next tracks
Cosine distance in the 80-dimensional embedding space
The Results
FS-VAE achieved "significant improvement in prediction distances for the next track played" compared to baseline methods (Spotify Research, 2022). The ablation study confirmed both components were essential—removing either slow or fast features degraded performance.
Real-World Deployment
While Spotify doesn't publish exact adoption figures, the research directly informed their recommendation systems. The company's ability to suggest music matching both general taste and current mood stems from these latent space techniques.
Key Insight
Separating timescales in latent space enables models to capture multi-scale patterns. Users aren't just "jazz fans"—they're "jazz fans currently wanting something upbeat." FS-VAE's latent representation captures both.
Case Study: OpenAI's Language Embeddings
Company: OpenAI
Models: text-embedding-3-small, text-embedding-3-large
Release Date: January 25, 2024
Benchmark: MTEB (Massive Text Embedding Benchmark), MIRACL (Multilingual Retrieval)
The Challenge
Language models need to convert text into numerical representations that capture semantic meaning. Previous embedding models struggled with multilingual retrieval and required large storage for high-quality representations.
The Solution
OpenAI released two new embedding models with significant architectural improvements:
text-embedding-3-small:
1,536 dimensions (default)
5× cheaper than previous generation ($0.00002 vs. $0.0001 per 1K tokens)
44.0% average score on MIRACL (vs. 31.4% for ada-002)
62.3% average score on MTEB (vs. 61.0% for ada-002)
text-embedding-3-large:
3,072 dimensions (default)
Highest performance across benchmarks
Supports dimension reduction without sacrificing accuracy
Innovative Feature: Adaptive Dimensions
Both models support reducing output dimensions. Developers can request 256-dimensional embeddings from the 3,072-dimensional model while maintaining performance that "outperform[s] full-size embeddings from text-embedding-ada-002" (OpenAI, 2024).
This flexibility addresses the storage-performance tradeoff. Large organizations storing billions of embeddings can choose smaller dimensions for efficiency without losing accuracy.
The Results
Within months of release, over 70% of GPT-4 API requests used these new embeddings (OpenAI, 2024). Applications included:
Knowledge retrieval in ChatGPT
Semantic search in enterprise applications
Retrieval-Augmented Generation (RAG) systems
Measurable Impact
40% improvement in multilingual retrieval (31.4% → 44.0% on MIRACL)
80% cost reduction for equivalent performance (5× price decrease)
Flexible scaling from 256 to 3,072 dimensions based on needs
Key Insight
The latent embedding space represents semantic relationships. Words with similar meanings have vectors pointing in similar directions. This geometry enables powerful applications: semantic search, document clustering, question answering—all operating in this abstract latent representation.
Benefits of Using Latent Space
Latent space provides concrete advantages that translate to cost savings, better performance, and new capabilities.
1. Massive Computational Savings
Processing in latent space reduces computational requirements by 10× to 256×. Stable Diffusion's 48× compression means generating an image requires 48 times fewer calculations than pixel-space methods (Stable Diffusion Art, 2024).
Cost Impact: At scale, this translates to millions in infrastructure savings. Training a model on latent representations instead of raw pixels can reduce cloud computing bills by 90%.
2. Faster Inference
Smaller representations mean faster processing. IBM notes that latent space mappings enhance "the ability of machine learning models to understand and manipulate [data] while reducing computational requirements" (IBM, 2024).
Real-time applications become feasible. Stable Diffusion generates images in seconds on consumer GPUs—impossible with pixel-space methods.
3. Better Generalization
Latent spaces capture underlying structure, not surface patterns. This leads to better generalization on new data. A model trained on latent representations of cats can recognize cats it's never seen, having learned the essence of "cat-ness" rather than memorizing pixels.
4. Smooth Interpolation
Continuous latent spaces enable smooth transitions. In drug discovery, researchers can interpolate between two molecular structures to explore the chemical space systematically (Medium, 2023).
5. Semantic Organization
Similar items cluster naturally. This organization emerges from data, not explicit programming. Language embeddings group synonyms, image latent spaces cluster visually similar objects.
6. Anomaly Detection
Compression reveals outliers. An autoencoder trained on normal data will struggle to reconstruct anomalies, making the reconstruction error a powerful anomaly detection signal (V7 Labs, 2024).
7. Data Augmentation
Sampling from learned latent distributions generates realistic new data points. This addresses data scarcity problems in domains like medical imaging where collecting real samples is expensive.
Challenges and Limitations
Latent space techniques aren't without tradeoffs.
1. Interpretability
Latent dimensions don't correspond to human-understandable features. A dimension in GPT-3's 12,288-dimensional embedding space might encode some aspect of meaning, but exactly what remains unclear (Dugas, 2024).
Researchers struggle to answer: "What does dimension 4,832 represent?" This opacity complicates debugging and trust.
2. Information Loss
Compression always loses information. Stable Diffusion's VAE "does lose information since the original VAE did not recover the fine details" (Stable Diffusion Art, 2024). The decoder compensates by learning to paint fine details, but subtle information is still lost.
3. Training Complexity
Learning good latent representations requires massive datasets and computational resources. DALL-E trained on 250 million image-text pairs (GitHub - simonsanvil, 2024). Smaller organizations can't replicate this.
4. Latent Space Gaps
In models like VAEs, trained only on certain distributions, there can be regions of latent space that don't correspond to meaningful outputs. Sampling from these gaps produces nonsensical results.
CV-VAE researchers noted "there is still a minor discrepancy between the latent spaces" when trying to maintain compatibility across models (ArXiv CV-VAE, 2024).
5. Bias Amplification
If training data contains biases, the latent representation may amplify them. DALL-E 2 generated "higher numbers of men than women for requests that do not mention gender" due to training data biases (Wikipedia DALL-E, 2025).
6. Computational Requirements for Training
While inference in latent space is efficient, creating the latent space (training the encoder and decoder) remains computationally intensive. Training DALL-E would "cost more than a hundred thousands of dollars" for most organizations (GitHub - simonsanvil, 2024).
Latent Space vs. Feature Space vs. Embedding Space
These terms are often used interchangeably, but they have distinct meanings.
Latent Space
Definition: The compressed, hidden representation learned by unsupervised models like autoencoders. "Latent" means hidden—these dimensions don't directly correspond to observable features.
Example: A VAE's bottleneck layer representing an image in 512 abstract dimensions.
Key Property: Unsupervised learning discovers the structure without labeled examples.
Feature Space
Definition: The space of meaningful features extracted from data. Can be hand-engineered or learned. IBM notes: "The feature space is the vector space associated with the range of possibilities not for data points but for the values of meaningful features" (IBM, 2024).
Example: For images, features might include edge orientations, textures, or color histograms.
Key Property: Often more interpretable than latent space—features can correspond to recognizable concepts.
Embedding Space
Definition: The high-dimensional space where data points are initially represented as vectors. This includes both input embeddings (like one-hot encodings) and learned embeddings (like word2vec).
Example: GPT-3's 12,288-dimensional embedding for each token (Dugas, 2024).
Key Property: Can be the starting point for further compression into latent space.
Comparison Table
Aspect | Latent Space | Feature Space | Embedding Space |
Origin | Learned by encoder | Extracted or designed | Input representation |
Supervision | Typically unsupervised | Can be supervised | Varies |
Interpretability | Low - abstract dimensions | Medium to high | Depends on method |
Dimensionality | Compressed (100-1000s) | Varies | Often high (1000s-10000s) |
Primary Use | Compression, generation | Classification, analysis | Neural network input |
Examples | VAE bottleneck, UMAP | HOG features, SIFT | Word embeddings, pixel vectors |
When Terms Overlap
IBM acknowledges: "'Feature space' and 'latent space' are often used interchangeably but aren't always synonymous" (IBM, 2024). The distinction blurs when:
Features are learned (not hand-designed)
Latent representations are interpretable
Embeddings are compressed
In practice, "latent space" emphasizes the hidden, learned nature, while "feature space" emphasizes the representation of meaningful properties.
Industry Impact and Market Statistics
Latent space techniques underpin the explosive growth of generative AI and modern machine learning.
Market Size
The global generative AI market, which heavily relies on latent space methods, has experienced unprecedented growth:
2024: $16.87 billion (Grand View Research, 2024)
2025 (projected): $22.20 billion to $59.01 billion depending on methodology (Grand View Research, 2024; Statista, 2024)
2030 (forecast): $109.37 billion (Grand View Research) to $400 billion (Statista)
2034 (forecast): $1,005.07 billion (Precedence Research, 2025)
The market is growing at a CAGR of 37-44%, one of the fastest growth rates in technology history (Grand View Research, 2024).
Regional Distribution
North America: Dominated with 40.8% market share in 2024 (Grand View Research, 2024). The United States leads due to concentration of AI research firms and venture capital.
Asia Pacific: Expected fastest growth at 27.6% CAGR from 2025-2034 (Precedence Research, 2025), driven by China, Japan, and South Korea's AI investments.
Europe: Second-largest market with 28% share (DemandSage, 2025), led by UK, Germany, and France.
Technology Adoption
By Component:
Software: 64.2% market share in 2024 (Grand View Research, 2024)
Services: Fastest growing at 44.7% CAGR due to integration complexity (Mordor Intelligence, 2025)
By Technology:
Transformers: 42% market share (Precedence Research, 2025)
VAEs/GANs: Significant portion of image and audio generation
Diffusion Models: Rapidly growing, particularly for image synthesis
By Industry:
Media & Entertainment: 34% of market (Precedence Research, 2025)
Business & Financial Services: 14%, growing fastest at 36.4% CAGR (Precedence Research, 2025)
Healthcare: Projected 37.1% CAGR through 2030 (Mordor Intelligence, 2025)
Usage Statistics
4 billion+ prompts issued daily across major LLM platforms (Founders Forum Group, 2025)
Over 70% of GPT-4 requests use the Turbo model with advanced embeddings (OpenAI, 2024)
300+ enterprise tools have embedded generative AI via APIs (Founders Forum Group, 2025)
ChatGPT reached 100 million users in 2 months (DemandSage, 2025)
Investment and Economic Impact
$107 billion deployed globally into AI startups in 2025 (Founders Forum Group, 2025)
26% of all global VC funding goes to AI startups (Founders Forum Group, 2025)
Generative AI expected to drive $1.3 trillion in annual economic impact by 2030 (Founders Forum Group, 2025)
Job Market Impact
97 million jobs expected to be created by AI by 2025 (World Economic Forum, cited in Founders Forum Group, 2025)
85 million jobs displaced, creating a net gain of 12 million jobs
Significant workforce transformation as repetitive tasks are automated and new AI-related roles emerge
Company Examples
OpenAI: Over 3 million people using DALL-E, generating 4 million images daily by 2022 (OpenAI API, 2024)
Spotify: Deployed VAE-based recommendation systems serving 500+ million users
Stability AI: Stable Diffusion downloaded millions of times, running on consumer hardware worth under $1,000
Microsoft: Integrated DALL-E into Designer app and Bing Image Creator
Step-by-Step: Creating a Simple Latent Space
Here's a practical guide to building a basic autoencoder that learns a latent representation.
Step 1: Gather Your Dataset
Choose a dataset with consistent structure. For this example, we'll use 28×28 grayscale images from MNIST (handwritten digits).
What you need:
60,000 training images
Each image: 28×28 = 784 pixels
Values: 0-255 (grayscale intensity)
Step 2: Normalize Your Data
Convert pixel values from 0-255 to 0-1 range:
X_train = X_train.astype('float32') / 255.0This helps neural networks train more efficiently.
Step 3: Design the Encoder
Create a neural network that compresses 784 dimensions to a smaller latent space (e.g., 32 dimensions):
from tensorflow import keras
from tensorflow.keras import layers
# Input layer
encoder_input = keras.Input(shape=(784,))
# Hidden layers progressively compress
x = layers.Dense(256, activation='relu')(encoder_input)
x = layers.Dense(128, activation='relu')(x)
# Latent space (32 dimensions)
latent = layers.Dense(32, activation='relu')(x)
encoder = keras.Model(encoder_input, latent)Step 4: Design the Decoder
Create the reverse process, expanding from 32 dimensions back to 784:
# Latent input
decoder_input = keras.Input(shape=(32,))
# Hidden layers progressively expand
x = layers.Dense(128, activation='relu')(decoder_input)
x = layers.Dense(256, activation='relu')(x)
# Output layer (784 pixels)
decoder_output = layers.Dense(784, activation='sigmoid')(x)
decoder = keras.Model(decoder_input, decoder_output)Step 5: Combine into Autoencoder
Chain encoder and decoder:
autoencoder_input = keras.Input(shape=(784,))
encoded = encoder(autoencoder_input)
decoded = decoder(encoded)
autoencoder = keras.Model(autoencoder_input, decoded)Step 6: Define the Loss Function
Use reconstruction loss (how different is output from input):
autoencoder.compile(
optimizer='adam',
loss='binary_crossentropy' # Measures reconstruction error
)Step 7: Train the Model
Train the autoencoder to minimize reconstruction error:
autoencoder.fit(
X_train, X_train, # Input = target (reconstruction)
epochs=50,
batch_size=256,
validation_split=0.1
)Step 8: Extract Latent Representations
Use the trained encoder to compress new images:
latent_representation = encoder.predict(X_test[0:10])
print(latent_representation.shape) # (10, 32)Each image is now represented by just 32 numbers instead of 784.
Step 9: Visualize the Latent Space
If using 2D latent space, plot the representations:
import matplotlib.pyplot as plt
latent_2d = encoder.predict(X_test)
plt.scatter(latent_2d[:, 0], latent_2d[:, 1], c=y_test, cmap='tab10')
plt.colorbar()
plt.show()You'll see different digit classes clustering in different regions.
Step 10: Generate New Images
Sample random points in latent space and decode:
import numpy as np
# Sample random latent vectors
random_latent = np.random.normal(size=(10, 32))
# Decode to images
generated_images = decoder.predict(random_latent)Results Interpretation
Compression ratio: 784 / 32 = 24.5× compression
Clustering: Similar digits have nearby latent representations
Interpolation: Moving smoothly through latent space creates smooth digit transitions
Generation: Sampling random latent vectors produces digit-like images
Limitations of This Simple Approach
This basic autoencoder has issues:
Generated images may be blurry
Latent space might have "holes" (regions not corresponding to valid digits)
No control over what features each latent dimension represents
Improvements:
Use Variational Autoencoder (VAE) for smoother latent space
Add convolutional layers for images
Increase latent dimensions for higher quality
Use perceptual loss instead of pixel-wise loss
Common Myths About Latent Space
Myth 1: "Latent space is just dimensionality reduction"
Reality: While latent space involves dimensionality reduction, it's not just compression—it's about learning meaningful, structured representations. PCA reduces dimensions, but latent spaces from neural networks capture non-linear relationships PCA can't.
The structure matters as much as the size. A good latent space organizes similar items together, enables smooth interpolation, and supports generation—properties simple dimensionality reduction doesn't guarantee.
Myth 2: "All dimensions in latent space are equally important"
Reality: Some dimensions capture more variation than others. In PCA, the first principal component explains the most variance. In neural network latent spaces, some dimensions are more active than others.
Researchers found that "the correlation dimension D2 remains consistent across different vocabulary subsets" in GPT-2 embeddings (MDPI, 2024), suggesting underlying structure in how dimensions are used.
Myth 3: "Latent space is completely interpretable"
Reality: Latent dimensions are mostly abstract. While some research has identified interpretable directions (e.g., "smiling" in face generation), most dimensions encode complex, entangled features.
IBM acknowledges this opacity: "The latent space typically omits information from dimensions of the embedding space that don't contain any features" (IBM, 2024), but what exactly each dimension captures often remains unclear.
Myth 4: "Bigger latent space is always better"
Reality: There's a tradeoff. Larger latent spaces capture more information but require more computation and may overfit to training data. Smaller spaces force better generalization but lose detail.
OpenAI's embeddings offer flexibility: text-embedding-3-large can be reduced from 3,072 to 256 dimensions while still "outperform[ing] full-size embeddings from text-embedding-ada-002" (OpenAI, 2024).
Myth 5: "Latent space only works for images"
Reality: Latent space techniques apply to any data type: text, audio, video, molecules, time series. Spotify uses VAEs for music (Spotify Research, 2022), OpenAI for language (OpenAI, 2024), and MIT for drug discovery (Medium, 2023).
The mathematics is domain-agnostic. Any high-dimensional data can benefit from latent compression.
Myth 6: "You can't control what latent space learns"
Reality: While vanilla autoencoders learn uncontrolled features, techniques like β-VAE, disentangled representation learning, and conditional VAEs give researchers control over what latent dimensions represent.
In β-VAE, adjusting β encourages learning disentangled representations where each dimension captures a single factor of variation (ArXiv - Netflix paper, 2024).
Myth 7: "Latent space is a new invention"
Reality: The core concept dates to the 1930s with PCA. What's new is the ability to learn complex, non-linear latent spaces with neural networks. Modern deep learning made latent space techniques practical at scale, but the mathematics has deep roots.
Future of Latent Space Technology
Latent space research is evolving rapidly with several promising directions.
1. Latent Reasoning
Recent research explores whether language models can "think" in latent space rather than generating explicit reasoning chains. COCONUT (Chain of Continuous Thought), presented at ICLR 2025, uses "continuous thought" encoded in the model's hidden states rather than tokens (OpenReview, 2024).
Results show latent reasoning can outperform chain-of-thought on some logical tasks while generating fewer tokens. The continuous latent thought "can encode multiple potential next reasoning steps, allowing the model to perform a breadth-first search" (OpenReview, 2024).
This suggests a future where AI models reason internally in abstract latent representations, only converting to language when communicating with humans.
2. Multimodal Latent Spaces
Current systems often use separate latent spaces for text, images, and audio. Future models will likely use unified latent spaces representing all modalities.
OpenAI's GPT-4 with vision hints at this direction. Gemini 2.0's "natively voice and vision multimodal" design points toward merged latent representations (Latent Space podcast, 2024).
3. Interpretable Latent Dimensions
Researchers are developing techniques to make latent dimensions more interpretable. β-VAE and its variants encourage disentangled representations where each dimension corresponds to a single, meaningful factor.
Success here would enable precise control: "Make this image more blue" by adjusting dimension 47, "Make this music faster" by modifying dimension 132.
4. Smaller, More Efficient Models
The trend toward smaller latent spaces without losing quality continues. Compression research focuses on maintaining performance while reducing dimensions.
Small Language Models (SLMs) trained on carefully curated data may outperform larger models, with more efficient latent representations (Globe Newswire, 2025).
5. Latent Space Optimization
Using latent spaces for optimization is gaining traction. The paper "Define latent spaces by example" (ArXiv, 2025) proposes creating targeted low-dimensional latent spaces for specific optimization tasks without losing generation fidelity.
Applications include protein design, drug discovery, and molecular optimization—fields where exploring the space of possibilities is computationally prohibitive without efficient latent representations.
6. Adaptive Latent Dimensions
OpenAI's approach of allowing variable embedding dimensions (256 to 3,072) points toward adaptive systems that allocate latent capacity based on complexity. Simple concepts use fewer dimensions; complex ones use more.
This could enable more efficient models that don't waste capacity on simple inputs.
7. Latent Space for Reinforcement Learning
Using latent space for data assimilation and reinforcement learning is emerging. Research published in 2024 on "A latent space method with maximum entropy deep reinforcement learning" showed that operating in latent space makes DRL "suitable for high-dimensional history matching problems" (ScienceDirect, 2024).
Future RL agents may learn and plan entirely in learned latent representations of their environment.
Frequently Asked Questions
Q1: How is latent space different from hidden layers in neural networks?
A: Hidden layers are intermediate processing steps in a neural network. Latent space specifically refers to a compressed representation—usually the bottleneck layer in an autoencoder—designed to capture essential features. All latent spaces involve hidden layers, but not all hidden layers are latent spaces.
Q2: Can you visualize high-dimensional latent space?
A: Yes, using dimensionality reduction techniques like t-SNE or UMAP. These project high-dimensional latent vectors (e.g., 512 dimensions) onto 2D or 3D plots. However, the visualization necessarily loses information—you're seeing a projection, not the full structure.
Q3: Why don't we just make latent space 2D or 3D for easy visualization?
A: Very low-dimensional latent spaces lose too much information. Complex data like images need hundreds of dimensions to capture all meaningful variations. A 2D latent space for faces might capture "age" and "gender" but miss thousands of other features like expression, pose, lighting, ethnicity.
Q4: How do I choose the right latent space size?
A: It's a tradeoff based on your application. Start with dimensionality 5-10% of your input size. For 28×28 images (784 pixels), try 32-128 dimensions. Then adjust:
Increase if reconstructions are poor or generations lack detail
Decrease if overfitting, or if you need faster inference/less storage
Validation performance guides the choice.
Q5: Can latent space be discrete instead of continuous?
A: Yes. VQ-VAE (Vector Quantized VAE) uses discrete latent codes from a learned codebook. DALL-E uses discrete tokens (1,024 integers from a vocabulary of 8,192). Discrete latent spaces enable autoregressive generation but sacrifice smooth interpolation.
Q6: What's the relationship between latent space and transfer learning?
A: Pre-trained encoders create latent representations useful for downstream tasks. An image encoder trained on ImageNet learns latent features that work for medical imaging, satellite imagery, etc. Transfer learning leverages these general-purpose latent representations.
Q7: Does latent space introduce bias?
A: Yes, if training data contains bias. The latent representation will encode those biases. DALL-E 2 exhibited gender bias (generating more men than women for neutral prompts) because the training data was imbalanced (Wikipedia DALL-E, 2025). Addressing bias requires curating training data or applying debiasing techniques.
Q8: Can I control what each latent dimension represents?
A: Standard autoencoders learn uncontrolled, entangled representations. Specialized techniques like β-VAE, disentangled VAE, or supervised methods can encourage interpretable dimensions. However, full control remains challenging—latent dimensions typically encode combinations of features.
Q9: How much data do I need to learn a good latent space?
A: It depends on complexity. Simple datasets (MNIST digits) need thousands of examples. Complex domains (natural images, language) need millions to billions. Stable Diffusion and DALL-E trained on hundreds of millions of images. Transfer learning can reduce requirements by using pre-trained encoders.
Q10: Why do some models use probabilistic latent spaces (VAEs) instead of deterministic (autoencoders)?
A: Probabilistic latent spaces (VAEs) enable generation by ensuring smooth, continuous distributions. You can sample random points and get realistic outputs. Deterministic autoencoders create latent spaces with "holes"—regions that don't correspond to valid data. VAEs fill these holes through their probabilistic structure.
Q11: Can latent space help with data privacy?
A: Potentially. Processing data in latent space can obscure raw details. However, latent representations still contain information that might be reconstructed or leaked. Privacy-preserving techniques like differential privacy can be applied to latent representations, but this is active research.
Q12: How do I debug when latent space isn't working?
A: Check:
Reconstruction quality: Can the decoder recover inputs from latent codes?
Latent space visualization: Do similar items cluster together?
Interpolation: Do intermediate latent points produce sensible outputs?
Loss curves: Is training converging?
Dimensionality: Try increasing/decreasing latent size
Common issues include too-small latent space (underfitting), too-large space (overfitting), or imbalanced loss terms in VAEs.
Key Takeaways
Latent space is the compressed, abstract representation that AI models use to capture essential data patterns while discarding redundancy—enabling a 512×512 image to be represented in 48 times fewer numbers.
Modern generative AI depends on latent space for efficiency. Without it, tools like Stable Diffusion, DALL-E, and ChatGPT wouldn't run on consumer hardware or respond in real-time.
The generative AI market reached $16.87 billion in 2024 and will grow to over $109 billion by 2030, with latent space techniques (VAEs, transformers, diffusion models) powering this growth (Grand View Research, 2024).
Real-world deployments deliver measurable results: Spotify's FS-VAE improved music recommendation accuracy, OpenAI's embeddings achieved 40% better multilingual retrieval, and Stable Diffusion reduced image generation costs by 98%.
Latent space enables capabilities impossible in raw data space: smooth interpolation between concepts, generation of new realistic samples, semantic organization, and anomaly detection.
The tradeoff is complexity vs. interpretability: While latent representations are efficient, understanding what each dimension represents remains challenging, limiting debugging and trust.
Future directions include latent reasoning, multimodal unification, and adaptive dimensionality—moving toward AI systems that think in abstract latent representations rather than explicit symbols.
Practical applications span all data types: images (Stable Diffusion), text (OpenAI embeddings), audio (Spotify recommendations), video (CV-VAE), and molecules (drug discovery).
The mathematics is accessible: Latent space fundamentally involves compression (encoder), representation (latent vector), and reconstruction (decoder)—concepts implementable in under 100 lines of code.
Industry adoption is accelerating: From 300+ enterprise tools embedding AI to billions in VC funding, latent space techniques are becoming infrastructure for the next generation of applications.
Actionable Next Steps
For Developers
Experiment with pre-trained models: Download Stable Diffusion's VAE, encode images to latent space, manipulate the latent vectors, and decode. See firsthand how compression works.
Build a simple autoencoder: Follow the step-by-step guide above using MNIST or your own dataset. Visualize the latent space and try interpolating between examples.
Explore OpenAI's embedding models: Use text-embedding-3-small or text-embedding-3-large to convert text into semantic latent representations. Build a semantic search or clustering application.
Study VAE implementations: Read the code for β-VAE, disentangled VAE, or Conditional VAE to understand advanced latent space techniques.
Attend to interpretability: Use techniques like t-SNE or UMAP to visualize your latent spaces. Understand what your model is learning.
For Business Leaders
Assess cost-benefit of latent space approaches: If you're processing high-dimensional data (images, text, audio), evaluate whether latent space compression could reduce infrastructure costs by 10-100×.
Explore vendor solutions: Major cloud providers (AWS, Google Cloud, Azure) offer pre-trained models with latent embeddings. Pilot projects require minimal investment.
Prioritize data quality over quantity: Latent space models learn from patterns in data. Biased or low-quality data produces biased latent representations. Invest in data curation.
Plan for the long term: The generative AI market is growing 37-44% annually. Building latent space expertise now positions your organization for the next decade.
For Researchers
Investigate interpretability: Despite progress, we still don't fully understand what latent dimensions encode. Research making latent spaces more interpretable could unlock new capabilities.
Explore multimodal latent spaces: Unified representations across text, image, audio, and video are the frontier. Methods that create coherent shared latent spaces will be highly impactful.
Address bias and fairness: Latent representations encode training data biases. Research on debiasing latent spaces or auditing for fairness is crucial.
Improve efficiency: Can we achieve the same quality with smaller latent dimensions? Can adaptive approaches allocate capacity where needed? These questions have practical impact.
Enable latent space optimization: Developing techniques to optimize objectives directly in latent space (design, discovery, planning) could revolutionize fields from drug development to materials science.
For Students
Master the fundamentals: Understanding autoencoders, VAEs, and PCA provides the foundation. Work through tutorials and implement models from scratch.
Read seminal papers: Kingma & Welling's VAE paper (2013), van den Oord's VQ-VAE (2017), Rombach's Latent Diffusion (2022). Understand the progression of ideas.
Experiment broadly: Try latent space techniques on different data types. Gain intuition for when they work well and when they struggle.
Contribute to open source: Implement improvements to existing models, add features to frameworks like Hugging Face or PyTorch.
Stay current: Follow conferences (NeurIPS, ICML, CVPR), blogs (Latent Space podcast, Sander Dieleman's blog), and company research (OpenAI, Google DeepMind, Anthropic).
Glossary
Autoencoder: A neural network that learns to compress data into a latent representation and then reconstruct it. Consists of an encoder and a decoder trained to minimize reconstruction error.
Bottleneck Layer: The narrowest layer in an autoencoder, representing the compressed latent space. Called a bottleneck because it forces information through a narrow channel.
Compression Ratio: The ratio between input dimensions and latent dimensions. Higher ratios mean more aggressive compression (e.g., 48× for Stable Diffusion).
Decoder: The part of an autoencoder that transforms latent representations back into observable data (images, text, audio).
Diffusion Model: A generative model that learns to remove noise from data. Latent diffusion models operate in compressed latent space rather than pixel space.
Dimensionality Reduction: Transforming high-dimensional data into lower dimensions while preserving important information. PCA and autoencoders both perform dimensionality reduction.
Embedding: A dense vector representation of data. Word embeddings map words to vectors; image embeddings map images to vectors. Often used interchangeably with latent representation.
Encoder: The part of an autoencoder that compresses input data into latent representations.
Generative Adversarial Network (GAN): A generative model using two competing networks. VQ-GAN combines this with vector quantized latent spaces.
Interpolation: Creating intermediate points between two data points by averaging their latent vectors. Enables smooth transitions.
KL Divergence: Kullback-Leibler divergence, a measure of difference between probability distributions. VAEs minimize KL divergence to encourage smooth latent spaces.
Latent Variable: A hidden variable not directly observed in the data but inferred by the model. Latent space consists of latent variables.
Principal Component Analysis (PCA): A classical technique for linear dimensionality reduction. Finds directions of maximum variance.
Reconstruction Loss: The error between original input and the autoencoder's reconstruction. Training minimizes this loss.
Sampling: Drawing random points from a distribution. In VAEs, sampling from the latent distribution generates new data.
Transformer: A neural network architecture based on attention mechanisms. GPT and other language models are transformers that use high-dimensional embedding spaces.
VAE (Variational Autoencoder): An autoencoder with probabilistic structure, learning latent distributions rather than fixed points. Enables smooth interpolation and generation.
Vector Quantization: Discretizing continuous vectors by mapping them to a fixed codebook of values. Used in VQ-VAE and DALL-E.
VQ-VAE: Vector Quantized Variational Autoencoder. Uses discrete latent codes from a learned codebook rather than continuous latent vectors.
Sources & References
Grand View Research (2024). Generative AI Market Size And Share | Industry Report, 2030. Retrieved from https://www.grandviewresearch.com/industry-analysis/generative-ai-market-report
Statista (2024). Generative AI - Worldwide | Market Forecast. Retrieved from https://www.statista.com/outlook/tmo/artificial-intelligence/generative-ai/worldwide
Precedence Research (2025). Generative AI Market Size to Hit USD 1005.07 Bn By 2034. Retrieved from https://www.precedenceresearch.com/generative-ai-market
IBM (2024). What Is Latent Space? - Machine learning. Retrieved from https://www.ibm.com/think/topics/latent-space
Metaschool (2024, November 1). Latent Space in Deep Learning: Concepts and Applications. Retrieved from https://metaschool.so/articles/latent-space-deep-learning
Stable Diffusion Art (2024, June 9). How does Stable Diffusion work? Retrieved from https://stable-diffusion-art.com/how-stable-diffusion-work/
OpenAI (2021, January 5). DALL·E: Creating images from text. Retrieved from https://openai.com/index/dall-e/
OpenAI (2024, January 25). New embedding models and API updates. Retrieved from https://openai.com/index/new-embedding-models-and-api-updates/
OpenAI (2024, November). DALL·E API now available in public beta. Retrieved from https://openai.com/index/dall-e-api-now-available-in-public-beta/
Wikipedia (2025, November 6). Stable Diffusion. Retrieved from https://en.wikipedia.org/wiki/Stable_Diffusion
Wikipedia (2025, November 6). DALL-E. Retrieved from https://en.wikipedia.org/wiki/DALL-E
Spotify Research (2022, February 28). Variational User Modeling with Slow and Fast Features. Retrieved from https://research.atspotify.com/publications/variational-user-modeling-with-slow-and-fast-features/
Spotify Research (2022, February). Modeling Users According to Their Slow and Fast-Moving Interests. Retrieved from https://research.atspotify.com/2022/02/modeling-users-according-to-their-slow-and-fast-moving-interests
Sander Dieleman (2025, April 15). Generative modelling in latent space. Retrieved from https://sander.ai/2025/04/15/latents.html
NVIDIA NeMo (2024). Stable Diffusion — NVIDIA NeMo Framework User Guide. Retrieved from https://docs.nvidia.com/nemo-framework/user-guide/24.09/nemotoolkit/multimodal/text2img/sd.html
ArXiv (2024, May 30). CV-VAE: A Compatible Video VAE for Latent Generative Video Models. Retrieved from https://arxiv.org/abs/2405.20279
ArXiv (2024, November 10). Improved Video VAE for Latent Video Diffusion Model. Retrieved from https://arxiv.org/html/2411.06449v1
OpenReview (2024, October 4). Training Large Language Model to Reason in a Continuous Latent Space. Retrieved from https://openreview.net/forum?id=tG4SgayTtk
ArXiv (2025, September 28). Define latent spaces by example: optimisation over the outputs of generative models. Retrieved from https://arxiv.org/html/2509.23800v1
ScienceDirect (2024, August 31). A latent space method with maximum entropy deep reinforcement learning for data assimilation. Retrieved from https://www.sciencedirect.com/science/article/abs/pii/S2949891024006456
V7 Labs (2024). Autoencoders in Deep Learning: Tutorial & Use Cases. Retrieved from https://www.v7labs.com/blog/autoencoders-guide
Medium (2023, October 24). Unveiling the World of Variational Autoencoders (VAEs). By Aadhityaa S B. Retrieved from https://medium.com/@aadhi0612/unveiling-the-world-of-vaes-c2c5802b5830
MDPI (2024, October 17). Fractal Analysis of GPT-2 Token Embedding Spaces: Stability and Evolution of Correlation Dimension. Retrieved from https://www.mdpi.com/2504-3110/8/10/603
Dugas.ch (2024). The GPT-3 Architecture, on a Napkin. Retrieved from https://dugas.ch/artificial_curiosity/GPT_architecture.html
InfoQ (2024, February 6). OpenAI Releases New Embedding Models and Improved GPT-4 Turbo. By Anthony Alford. Retrieved from https://www.infoq.com/news/2024/02/openai-model-updates/
DataCamp (2024, March 15). Exploring Text-Embedding-3-Large: A Comprehensive Guide to the new OpenAI Embeddings. Retrieved from https://www.datacamp.com/tutorial/exploring-text-embedding-3-large-new-openai-embeddings
GitHub - simonsanvil (2024). DALL-E-Explained: Description and applications of OpenAI's paper about DALL-E (2021). Retrieved from https://github.com/simonsanvil/DALL-E-Explained
Latent Space Podcast (2024, December 27). The 2025 AI Engineering Reading List. Retrieved from https://www.latent.space/p/2025-papers
Latent Space Podcast (2024, December 31). Latent.Space 2024 Year in Review. Retrieved from https://www.latent.space/p/2024-review
Founders Forum Group (2025, July 14). AI Statistics 2024–2025: Global Trends, Market Growth & Adoption Data. Retrieved from https://ff.co/ai-statistics-trends-global-market/
Mordor Intelligence (2025, June 18). Generative AI Market Size, Growth Analysis & Industry Forecast, 2030. Retrieved from https://www.mordorintelligence.com/industry-reports/generative-ai-market
GM Insights (2025, July 1). Generative AI solution Market Size Report, 2025 – 2034. Retrieved from https://www.gminsights.com/industry-analysis/generative-ai-solution-market
DemandSage (2025, September 5). 51 Generative AI Statistics 2025 (Market Size & Reports). Retrieved from https://www.demandsage.com/generative-ai-statistics/
Globe Newswire (2025, April 10). Generative AI Market Size Expected to Reach USD 1,005.07 Bn By 2034. Retrieved from https://www.globenewswire.com/news-release/2025/04/10/3059463/0/en/
ABI Research (2024, July 25). Artificial Intelligence (AI) Software Market Size: 2024 to 2030. Retrieved from https://www.abiresearch.com/news-resources/chart-data/report-artificial-intelligence-market-size-global
Markets and Markets (2025). Generative AI Market Size, Trends, & Technology Roadmap. Retrieved from https://www.marketsandmarkets.com/Market-Reports/generative-ai-market-142870584.html
JIPD (2024, August 26). Leveraging variational autoencoders and recurrent neural networks for demand forecasting in supply chain management: A case study. Retrieved from https://systems.enpress-publisher.com/index.php/jipd/article/view/6639
SkAI Institute (2024). Project 10: Interpretable Latent Space Generative Models for Galaxy Evolution. Retrieved from https://skai-institute.org/skai-funded-projects-year-1-2024-25-and-year-2-2025-26/
Rechtsmedizin (2025, March 3). Latent spaces of generative models for forensic age estimation. Retrieved from https://link.springer.com/article/10.1007/s00194-025-00745-9
CVPR (2024). Smooth Diffusion: Crafting Smooth Latent Spaces in Diffusion Models. Retrieved from https://openaccess.thecvf.com/content/CVPR2024/papers/Guo_Smooth_Diffusion_Crafting_Smooth_Latent_Spaces_in_Diffusion_Models_CVPR_2024_paper.pdf
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