{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/spontaneous-symmetry-breaking-in-generative-1","title":"Spontaneous Symmetry Breaking in Generative Diffusion Models","arxiv_id":"2305.19693","date":"2023-05-31","proceeding":"NeurIPS 2023 11","authors":["Gabriel Raya","Luca Ambrogioni"],"abstract":"Generative diffusion models have recently emerged as a leading approach for generating high-dimensional data. In this paper, we show that the dynamics of these models exhibit a spontaneous symmetry breaking that divides the generative dynamics into two distinct phases: 1) A linear steady-state dynamics around a central fixed-point and 2) an attractor dynamics directed towards the data manifold. These two \"phases\" are separated by the change in stability of the central fixed-point, with the resulting window of instability being responsible for the diversity of the generated samples. Using both theoretical and empirical evidence, we show that an accurate simulation of the early dynamics does not significantly contribute to the final generation, since early fluctuations are reverted to the central fixed point. To leverage this insight, we propose a Gaussian late initialization scheme, which significantly improves model performance, achieving up to 3x FID improvements on fast samplers, while also increasing sample diversity (e.g., racial composition of generated CelebA images). Our work offers a new way to understand the generative dynamics of diffusion models that has the potential to bring about higher performance and less biased fast-samplers.","url_abs":"https://arxiv.org/abs/2305.19693v3","url_pdf":"https://arxiv.org/pdf/2305.19693v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"spontaneous-symmetry-breaking-in-generative-1","repo_url":"https://github.com/gabrielraya/symmetry_breaking_diffusion_models","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"jax","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"diversity","task_name":"Diversity"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2305.19693","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2305.19693"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"deterministic:regex_extraction","url":"https://github.com/gabrielraya/symmetry_breaking_diffusion_models","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran":4,"ran_draft_wrong":2,"unverified":13},"by_repo_kind":{"official":{"samples":19,"ran":6,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"04548c6c9fff2b3f","entry":"default_init","repo":"gabrielraya/symmetry_breaking_diffusion_models","repo_kind":"official","path":"models/layers.py","file_url":"https://github.com/gabrielraya/symmetry_breaking_diffusion_models/blob/HEAD/models/layers.py","link_basis":"plan_row","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"04548c6c9fff2b3f"}},{"code_sha256_prefix":"6c419026e778dee2","entry":"get_data_inverse_scaler","repo":"gabrielraya/symmetry_breaking_diffusion_models","repo_kind":"official","path":"datasets.py","file_url":"https://github.com/gabrielraya/symmetry_breaking_diffusion_models/blob/HEAD/datasets.py","link_basis":"harvester_set","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"6c419026e778dee2"}},{"code_sha256_prefix":"346d2e6cc8b48a5d","entry":"get_data_scaler","repo":"gabrielraya/symmetry_breaking_diffusion_models","repo_kind":"official","path":"datasets.py","file_url":"https://github.com/gabrielraya/symmetry_breaking_diffusion_models/blob/HEAD/datasets.py","link_basis":"harvester_set","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"346d2e6cc8b48a5d"}},{"code_sha256_prefix":"8ff7c24dade9904c","entry":"get_optimizer","repo":"gabrielraya/symmetry_breaking_diffusion_models","repo_kind":"official","path":"losses.py","file_url":"https://github.com/gabrielraya/symmetry_breaking_diffusion_models/blob/HEAD/losses.py","link_basis":"harvester_set","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"8ff7c24dade9904c"}},{"code_sha256_prefix":"366bb8c7035a2fc8","entry":"optimization_manager","repo":"gabrielraya/symmetry_breaking_diffusion_models","repo_kind":"official","path":"losses.py","file_url":"https://github.com/gabrielraya/symmetry_breaking_diffusion_models/blob/HEAD/losses.py","link_basis":"harvester_set","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"366bb8c7035a2fc8"}},{"code_sha256_prefix":"f34882fce4b22d20","entry":"variance_scaling","repo":"gabrielraya/symmetry_breaking_diffusion_models","repo_kind":"official","path":"models/layers.py","file_url":"https://github.com/gabrielraya/symmetry_breaking_diffusion_models/blob/HEAD/models/layers.py","link_basis":"plan_row","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"f34882fce4b22d20"}},{"code_sha256_prefix":"c4dd4187aa1e3c9d","entry":"create_model","repo":"gabrielraya/symmetry_breaking_diffusion_models","repo_kind":"official","path":"models/utils.py","file_url":"https://github.com/gabrielraya/symmetry_breaking_diffusion_models/blob/HEAD/models/utils.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"c4dd4187aa1e3c9d"}},{"code_sha256_prefix":"fd14d238ccd5f679","entry":"crop_resize","repo":"gabrielraya/symmetry_breaking_diffusion_models","repo_kind":"official","path":"datasets.py","file_url":"https://github.com/gabrielraya/symmetry_breaking_diffusion_models/blob/HEAD/datasets.py","link_basis":"plan_row","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"fd14d238ccd5f679"}},{"code_sha256_prefix":"899b121e3d100946","entry":"func","repo":"gabrielraya/symmetry_breaking_diffusion_models","repo_kind":"official","path":"diversity_eval.py","file_url":"https://github.com/gabrielraya/symmetry_breaking_diffusion_models/blob/HEAD/diversity_eval.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"899b121e3d100946"}},{"code_sha256_prefix":"6a23f5f1484e38c8","entry":"generate_xt_samples","repo":"gabrielraya/symmetry_breaking_diffusion_models","repo_kind":"official","path":"fast_sampler.py","file_url":"https://github.com/gabrielraya/symmetry_breaking_diffusion_models/blob/HEAD/fast_sampler.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"6a23f5f1484e38c8"}},{"code_sha256_prefix":"8232012f278d45f4","entry":"get_act","repo":"gabrielraya/symmetry_breaking_diffusion_models","repo_kind":"official","path":"models/layers.py","file_url":"https://github.com/gabrielraya/symmetry_breaking_diffusion_models/blob/HEAD/models/layers.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"8232012f278d45f4"}},{"code_sha256_prefix":"bec27c2f10409e37","entry":"get_approx_stats","repo":"gabrielraya/symmetry_breaking_diffusion_models","repo_kind":"official","path":"fast_sampler.py","file_url":"https://github.com/gabrielraya/symmetry_breaking_diffusion_models/blob/HEAD/fast_sampler.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"bec27c2f10409e37"}},{"code_sha256_prefix":"f394c103783c55c8","entry":"get_approx_stats_HQ","repo":"gabrielraya/symmetry_breaking_diffusion_models","repo_kind":"official","path":"fast_sampler.py","file_url":"https://github.com/gabrielraya/symmetry_breaking_diffusion_models/blob/HEAD/fast_sampler.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"f394c103783c55c8"}},{"code_sha256_prefix":"ecef6cc47991aad2","entry":"get_batch_activations","repo":"gabrielraya/symmetry_breaking_diffusion_models","repo_kind":"official","path":"fast_fid.py","file_url":"https://github.com/gabrielraya/symmetry_breaking_diffusion_models/blob/HEAD/fast_fid.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"ecef6cc47991aad2"}},{"code_sha256_prefix":"2cd0e1616c274ce4","entry":"get_batch_stats","repo":"gabrielraya/symmetry_breaking_diffusion_models","repo_kind":"official","path":"fast_fid.py","file_url":"https://github.com/gabrielraya/symmetry_breaking_diffusion_models/blob/HEAD/fast_fid.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"2cd0e1616c274ce4"}},{"code_sha256_prefix":"441bd52748d62295","entry":"get_data_stats","repo":"gabrielraya/symmetry_breaking_diffusion_models","repo_kind":"official","path":"fast_fid.py","file_url":"https://github.com/gabrielraya/symmetry_breaking_diffusion_models/blob/HEAD/fast_fid.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"441bd52748d62295"}},{"code_sha256_prefix":"b3e18524b8df81a1","entry":"get_model","repo":"gabrielraya/symmetry_breaking_diffusion_models","repo_kind":"official","path":"models/utils.py","file_url":"https://github.com/gabrielraya/symmetry_breaking_diffusion_models/blob/HEAD/models/utils.py","link_basis":"plan_row","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"b3e18524b8df81a1"}},{"code_sha256_prefix":"72cc7337a59b2a93","entry":"load_dataset_stats","repo":"gabrielraya/symmetry_breaking_diffusion_models","repo_kind":"official","path":"evaluation.py","file_url":"https://github.com/gabrielraya/symmetry_breaking_diffusion_models/blob/HEAD/evaluation.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"72cc7337a59b2a93"}},{"code_sha256_prefix":"79fcc0f38b056e86","entry":"register_model","repo":"gabrielraya/symmetry_breaking_diffusion_models","repo_kind":"official","path":"models/utils.py","file_url":"https://github.com/gabrielraya/symmetry_breaking_diffusion_models/blob/HEAD/models/utils.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"79fcc0f38b056e86"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}