[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86075-en":3,"doc-seo-86075-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86075,687197207057,"Sage","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Diversify Diffusion with Temperature Sampling and Variance-Corrective Time Shifting","Diffusion models replicate the training distribution but also its imbalances, making rare or under-represented modes difficult to generate. Temperature sampling addresses this by sampling from a high-temperature tempered target p0(γ)(x)∝p0(x)γ with 0\u003Cγ\u003C1 to flatten dominant modes and boost rare events. Naive score scaling reweights modes yet inflates per-mode variance, breaking reverse diffusion and degrading quality. Variance-corrective time shifting fixes this training-free by querying a shifted timestep and scaling the score by γ, preserving diversity gains while maintaining sample fidelity and condition consistency across diffusion backbones.","Diversify Diffusion with Temperature Sampling and Variance-Corrective Time Shifting  \nPeizhuo Li  \nETH Zurich  \nEmre Aksan  \nGoogle  \nAlexandru-Eugen Ichim  \nGoogle  \nThabo Beeler Olga Sorkine-Hornung  \nGoogle ETH Zurich  \narXiv :2607 . 10853v1 [ cs .CV] 12 Jul 2026  \nFigure 1: Left: The effect of increasing temperature (i.e. lowering γ) on a 1D Gaussian mixture. Middle: Sampling results with prompt “an astronaut on the moon” using Stable Diffusion. Right: The effect of our method on the same prompt and model.  \nAbstract  \nDiffusion models faithfully reproduce their training distribution, but also inherit its imbalances and leave rare or under-represented modes hard to reach. A natural inference-time remedy is to sample from the high-temperature target p0(γ)(x) ∝ p0 (x)γ for 0 \u003C γ \u003C 1, which flattens dominant modes and lifts rare ones. However, naive score scaling while correctly reweighting modes also inflates the per-mode variance, breaking the reverse diffusion process and degrading sample quality.  \nWe introduce variance-corrective time shifting, a training-free fix that queries the network at a shifted timestep and scales the resulting score by γ, canceling the variance inflation while preserving the mode reweighting. The correction turns simple temperature sampling into a practical diversity knob for pretrained diffusion and flow-matching backbones with no retraining, and we demonstrate consistent gains at minimal cost to sample quality and condition fidelity across DiT, Stable Diffusion and Motion Diffusion models. We further show that the timing of the temperature intervention enables coarse-to-fine control: high-noise stages drive compositional diversity across modes, while low-noise stages drive local appearance variation under a fixed composition.  \n1 Introduction  \nDiffusion models [11, 31, 33] have emerged as the dominant paradigm for generative modeling across images, video and 3D content. Beyond their high quality output, another key strength of diffusion models is that they offer a flexible inference-time control mechanism [10], which allows users to steer the sampling process without retraining the model. Yet, their samples often reflect the biases of  \nPreprint.  \nthe data they are trained on: common modes are reproduced reliably, while rare or under-represented modes are unlikely to be generated. Although this behavior aligns the goal for matching the training distribution, the lack of diversity could be problematic in creative settings, where users care about exploring multiple plausible outcomes rather than a single output.  \nA natural way to surface rare modes is to draw from the high-temperature target  \np0(γ)(x) := p0Z(xγ)γ , Zγ := Zp0 (x)γ dx, (1)  \nwhich flattens dominant modes and boosts the relative probability of rare events for 0 \u003C γ \u003C 1, as shown in Fig. 1 (left) . Here, p0 (x) is the original data distribution and γ is the inverse temperature parameter that controls the strength of the effect, with γ = 1 recovering the original distribution and γ → 0 approaching a uniform distribution, i.e. infinitely high temperature. In diffusion models, a neural network learns the score, the logarithmic likelihood gradient, and gradually denoises the random distribution pT (x) to the data distribution p0 (x) guided by the score. The temperature sampling looks deceptively simple on score: the identity ∇x log p0(γ)(x) = γ ∇x log p0 (x) holds strictly and conveniently cancels the unknown normalizer Zγ . One might therefore hope to obtain p (γ) by multiplying the learned score by γ throughout the reverse diffusion process.  \nHowever, naive score scaling conflates two effects. It achieves the macroscopic goal of reweighting modes, but it also induces an unwanted microscopic variance expansion that introduces more noise than expected, as demonstrated in Fig. 1 (left) . The excess variance breaks the strict correspondence between the score of the noised tempered marginal ∇x log pt(γ)(x) and the reverse diffusion pro","cbCaibTGxaUCexq7","https://ap.wps.com/l/cbCaibTGxaUCexq7","pdf",47007559,4,1,19,"English","en",105,"# Introduction\n## Temperature sampling for diversity\n## Variance inflation from naive score scaling\n## Variance-corrective time shifting\n## Stage-wise (coarse-to-fine) temperature control","[{\"question\":\"Why does temperature sampling improve diversity in diffusion models?\",\"answer\":\"Sampling from a tempered target p0(γ)(x)∝p0(x)γ with 0\\u003cγ\\u003c1 flattens dominant modes and increases the relative probability of rare events, producing more diverse outputs.\"},{\"question\":\"What goes wrong with naive score scaling during reverse diffusion?\",\"answer\":\"Naive scaling both reweights modes and inflates per-mode variance, which breaks the correspondence needed for the reverse diffusion process and leads to lower-quality, off-manifold, blurry samples.\"},{\"question\":\"How does variance-corrective time shifting enable a training-free fix?\",\"answer\":\"It queries the network at a shifted timestep with a smaller noise level and scales the resulting score by γ, canceling variance inflation while preserving the intended mode reweighting.\"}]",1784208364,48,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"diversify-diffusion-with-temperature-sampling-and-variance-corrective-time-shifting","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":20},"https://docshare.wps.com/document/diversify-diffusion-with-temperature-sampling-and-variance-corrective-time-shifting/86075/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-24","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why does temperature sampling improve diversity in diffusion models?","Question",{"text":75,"@type":76},"Sampling from a tempered target p0(γ)(x)∝p0(x)γ with 0\u003Cγ\u003C1 flattens dominant modes and increases the relative probability of rare events, producing more diverse outputs.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What goes wrong with naive score scaling during reverse diffusion?",{"text":80,"@type":76},"Naive scaling both reweights modes and inflates per-mode variance, which breaks the correspondence needed for the reverse diffusion process and leads to lower-quality, off-manifold, blurry samples.",{"name":82,"@type":73,"acceptedAnswer":83},"How does variance-corrective time shifting enable a training-free fix?",{"text":84,"@type":76},"It queries the network at a shifted timestep with a smaller noise level and scales the resulting score by γ, canceling variance inflation while preserving the intended mode 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