An analytic theory of creativity in convolutional diffusion models

2024/12/28 by Mason Kamb, Surya Ganguli, Kamb, Mason +1 · 16 voices · 26 citations
Psychology · #Creativity in Education and Neuroscience #cond-mat.dis-nn #cs.AI #cs.LG #q-bio.NC #stat.ML

paper · pdf · doi:10.48550/arxiv.2412.20292

openalex publication_date 2024/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain an analytic, interpretable and predictive theory of creativity in convolutional diffusion models. Indeed, score-matching diffusion models can generate highly original images that lie far from their training data. However, optimal score-matching theory suggests that these models should only be able to produce memorized training examples. To reconcile this theory-experiment gap, we identify two simple inductive biases, locality and equivariance, that: (1) induce a form of combinatorial creativity by preventing optimal score-matching; (2) result in fully analytic, completely mechanistically interpretable, local score (LS) and equivariant local score (ELS) machines that, (3) after calibrating a single time-dependent hyperparameter can quantitatively predict the outputs of trained convolution only diffusion models (like ResNets and UNets) with high accuracy (median r² of 0.95, 0.94, 0.94, 0.96 for our top model on CIFAR10, FashionMNIST, MNIST, and CelebA). Our model reveals a locally consistent patch mosaic mechanism of creativity, in which diffusion models create exponentially many novel images by mixing and matching different local training set patches at different scales and image locations. Our theory also partially predicts the outputs of pre-trained self-attention enabled UNets (median r² ∼ 0.77 on CIFAR10), revealing an intriguing role for attention in carving out semantic coherence from local patch mosaics.

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• A Closer Look at Model Collapse: From a Generalization-to-Memorization Perspective
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• Locality in Image Diffusion Models Emerges from Data Statistics
• Local Diffusion Models and Phases of Data Distributions

Discussions

• Our new paper! "Analytic theory of creativity in convolutional diffusion models" lead expertly by @masonkamb.bsky.social arxiv.org/abs/2412.20292 Our closed-form theory needs no training, is mechanis [bsky, 134 points, 5 comments]
• Excited to finally share this work w/ @suryaganguli.bsky.social Tl;dr: we find the first closed-form analytical theory that replicates the outputs of the very simplest diffusion models, with median pi [bsky, 107 points, 3 comments]
• Bravo 👏 An analytic theory of creativity in convolutional diffusion models by Kamb & Ganguli I’ve wondered about this very problem for two years now, with wispy intuition that points to exactly thi [bsky, 15 points, 0 comments]
• An analytic theory of creativity in convolutional diffusion models [hn, 7 points, 0 comments]
• Compositional generalization might just be one piece of the puzzle. Here's a nice paper on this (but for diffusion): arxiv.org/abs/2412.20292. The point is there are many ways LLMs might generalize f [bsky, 5 points, 0 comments]
• Image diffusion models glue together patches from training images arxiv.org/abs/2412.20292 [bsky, 4 points, 0 comments]
• @lynncole.bsky.social Turns out, not all diffusion models "steal" after all: arxiv.org/abs/2412.20292 [bsky, 3 points, 1 comments]
• An analytic theory of creativity in convolutional diffusion models [hn, 3 points, 0 comments]
• An analytic theory of creativity in convolutional diffusion models [hn, 2 points, 0 comments]
• #MLSky Direct link to the study: arxiv.org/abs/2412.20292 [bsky, 2 points, 0 comments]
• An analytical theory of creativity in convolutional diffusion models [via Cornell Uni] 🧪🔬🤖🧠🖍️🎨 "a locally consistent [] mechanism of creativity, in which diffusion models create [] many novel im [bsky, 1 points, 1 comments]
• "An analytic theory of creativity in convolutional diffusion models" arxiv.org/abs/2412.20292 Image generation results predicted using analytical computations that required no training. #AI #ImageGene [bsky, 1 points, 0 comments]
• 拡散モデルは単純に考えると学習データのいずれか1つをそのまま確率的に出力するだけになりそうなのに、なぜ多様な出力が得られるのかという問題に対する論文。 arxiv.org/abs/2412.20292 www.quantamagazine.org/researchers-... 次の2点が重要なのではないかとのこと。 ・ニューラルネットワークが画像等の全体ではなく周辺の情報のみを元に出力を決めてい [bsky, 1 points, 1 comments]
• An analytic theory of creativity in convolutional diffusion models [hn, 1 points, 0 comments]
• New paper: ‘An Analytic Theory of Creativity in Convolutional Diffusion Models’ explores how diffusion models generate creative outputs by combining training data patches. A groundbreaking foundation [bsky, 0 points, 0 comments]
• @kortizart.bsky.social, this paper might interest you: arxiv.org/abs/2412.20292 If you can get beyond the 'creativity' bs, it algorithmically predicts the output of diffusion models by interpreting th [bsky, 0 points, 0 comments]

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