Temporal Score Rescaling for Temperature Sampling

TL;DR

Temporal Score Rescaling (TSR) is a training-free, inference-time knob that rescales the predicted noise (or flow velocity) of any diffusion/flow model by a temperature parameter k to sharpen (k>1) or broaden (k<1) the sampled distribution. Unlike classifier-free guidance, TSR has no two-pass overhead and no extra conditioning branch; unlike the “constant noise scaling” baseline, it composes with deterministic samplers (Flow-ODE) and preserves the relative mode weights of the data distribution. The project page presents only synthetic 2D-Gaussian-mixture experiments and an interactive slider — no image/video benchmarks are reported.

Key claims

The TSR rescaling rule for an ε-prediction diffusion model replaces ε_θ(x,t) with a k- and noise-schedule-dependent scaled prediction; for a flow-matching model it replaces the velocity v_θ(x,t) analogously, defined in terms of α_t, σ_t and a user noise σ [Method].
At k=1 TSR is the identity, so any off-the-shelf pretrained diffusion or flow model can be sharpened or broadened post-hoc with no training and no extra inference compute [Method].
On a 2D mixture-of-6-Gaussians toy with class-conditional generation, TSR preserves the equal weights between modes belonging to the conditioned class as k varies, while Constant Noise Scaling (CNS) and Classifier-Free Guidance (CFG) both distort the inter-mode weights [Comparison with Prior Methods].
TSR is applicable to deterministic samplers (e.g. Flow-ODE) where CNS — the de facto “pseudo-temperature” trick — is not defined, because CNS perturbs the stochastic noise term that an ODE sampler does not have [Comparison with Prior Methods].

Method

TSR reinterprets the model’s output as a time-dependent score that can be rescaled by a factor that depends on the current timestep t, the noise schedule (α_t, σ_t), and the inverse temperature k. For ε-predictors the substitution is applied before subtracting the predicted noise from x_t; for flow-matching models the velocity is rescaled in the same family. No retraining or auxiliary network is required, and the cost per sampling step is unchanged. The project page exposes an interactive slider over k on synthetic distributions and compares the resulting density to (i) plain DDPM/Flow-ODE, (ii) CNS, and (iii) CFG.

Results

Quantitative results on the project page are limited to qualitative density plots over a 2D 6-mode Gaussian mixture. The headline visual finding is that TSR keeps the three class-1 modes at equal mass across a wide range of k, while CNS and CFG either lose modes or rebalance them as the temperature/guidance scale moves away from the default. No image/video/text benchmark numbers, FID/CLIPScore/VBench results, or wall-clock timings are reported on the page as fetched.

Why it’s interesting

TSR adds a new axis to the Classifier-Free Guidance variants cluster: rather than redesigning the guidance branches (SparkVSR’s Reference-Free Guidance, Normalized Attention Guidance: Universal Negative Guidance for Diffusion Models‘s attention-space NAG) or folding guidance into training (SoFlow: Solution Flow Models for One-Step Generative Modeling, Continuous Adversarial Flow Models), it leaves both the model and the conditioning untouched and instead rescales the single-pass score by a temperature. The CNS/CFG mode-collapse comparison is the load-bearing claim — if it holds on real data distributions (image/video) it would matter for video-generation products that currently use CFG-scale as a de-facto diversity knob and pay for it in oversaturated samples. The Slack-poster’s “results look lukewarm but may be a good one to test on ray3” note matches the page’s evidence: synthetic-only, no real-data ablation yet.