How regular is the model's internal temporal evolution?
模型内部的时间演化是否规律？
PROBLEM → COUNTEREXAMPLE → METHOD
从时间正则化到患者特异性动力学From Temporal Regularity to Patient-Specific Kinetics
稀疏 DCE 观测首先产生不确定性；可信区间带总结逐点可行性；反例再迫使我们讨论整条轨迹的一致性。Sparse DCE observations create uncertainty first. A credible band summarizes pointwise plausibility; the counterexample then motivates whole-trajectory consistency.
ε̂(t)Denoiser prediction
→
LDLTemporal regularity
→
ŷ(t)Kinetic signal
→
Band + TrajectoryPatient posterior
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研究动机：从时间正则化到患者特异性动力学Research Motivation: From Temporal Regularity to Patient-Specific Kinetics
Temporal regularity ≠ kinetic fidelity / 时间规律性不等于动力学保真度
Original CEKWorld
ε̂θ(t)denoiser prediction
噪声预测
噪声预测
LDLDτ2 ε̂θ
temporal regularity
temporal regularity
Î(t)generated MRI
生成图像
生成图像
ŷ(t)ROI / measurement
动力学信号
动力学信号
Bandpointwise plausibility
逐点可行性
逐点可行性
Trajectorywhole-trajectory coherence
整轨迹一致性
整轨迹一致性
Is the enhancement value plausible for this patient at this time?
该患者在这个时刻的增强值是否逐点可行？
Can all generated time points be jointly explained by one coherent patient-specific process?
所有生成时间点能否由一条患者特异性动力学过程共同解释？
Teaching takeawayLDL stays in denoiser-prediction space; the proposed Band and Trajectory terms operate after an explicit image-space measurement path.LDL 留在去噪器预测空间；拟议的 Band 与 Trajectory 项必须在显式图像测量路径之后定义。
MECHANISM EXPLORER · COMPLETE V3 BUILD
CEKWorld 多层时间约束机制演示器CEKWorld Temporal Guidance Mechanism Explorer
从去噪器预测空间一路追踪到患者特异性动力学轨迹空间，观察三层约束分别解决什么问题。Watch how temporal information moves from denoiser prediction space to patient-specific kinetic trajectory space.
Synthetic Mechanism DemonstrationChecking WebGL 2…
COMPARE MODE
同一合成患者下的四种时间约束Four Temporal-Constraint Modes on One Synthetic Patient
Qualitative synthetic mechanism levels, not clinical or experimental measurements.
SPLIT VIEW
同一 τdce 下的前后对照Synchronized Before / After at the Same τdce
BEFORE
—LDL only / 仅 LDL
LDL metric—
Band Loss—
Trajectory Loss—
AFTER
—LDL + Band + Trajectory
LDL metric—
Band Loss—
Trajectory Loss—
Both panels use the same fixed synthetic patient and the same τdce. Metric labels are qualitative teaching states, not fabricated study results.
GUIDED TOUR · 65 SECONDS
一分钟机制自动讲解1-Minute Mechanism Tour
02
LDL 实际作用在哪里？Where Does LDL Actually Operate?
Separate diffusion timestep s, DCE acquisition time tau_dce, and kinetic signal.
noise-prediction space / 噪声预测空间latent space / 潜在空间image space / 图像空间kinetic-signal space / 动力学信号空间
Source-code-confirmed interpretation默认 eps parameterization 下，LDL 约束的是
full_model_output = ε̂θ 沿 DCE acquisition time 的二阶变化。x0_pred_full 是 one-step clean latent estimate，不是 MRI 图像或最终多步 DDIM sample。03
五参数动力学模型Five-Parameter Kinetic Model
Phenomenological kinetic-shape parameters, not validated physiological parameters.
θ = (A, α, β, γ, q) · positivity-preserving range · stable near t = 0
peak / 峰值 —tpeak / 峰时 —
C(t; θ)Synthetic teaching example
kinetic shape / 动力学形状 observed phase / 观测相位
04
为什么 3–4 个观测不够？Why Are 3–4 Observations Not Enough?
Different parameter sets can explain the same sparse observations.
Sparse observations do not justify treating one fitted θ* as the patient's unique kinetic truth.橙色曲线由第 03 节五个滑块实时控制；候选按钮可载入另一组参数。稀疏观测不足以把某个拟合 θ* 当作患者唯一的动力学真值。
05
4 个点 vs 15 个点4 Points vs 15 Points
Dense observations generally narrow uncertainty, but uniqueness must be established rather than assumed.
Nobservations > Nparameters does not guarantee unique parameter identification.观测数超过参数数，不保证唯一识别。
06
从单一最佳拟合到患者后验From Single Best Fit to Patient Posterior
A best fit is one explanation; the posterior keeps explanations still supported by patient data.
当前只显示一条 single best fit。点击后展开 illustrative posterior。
Illustrative posterior / Synthetic demonstration当前页面没有用真实 cohort 拟合 Bayesian posterior；后验轨迹是可复现的教学数据。
07
后验轨迹族Posterior Trajectory Family
Sample a family of patient-supported trajectories, not a single asserted truth.
posterior candidates / 候选轨迹 median / 中位数 pointwise posterior credible band / 逐点后验可信区间带
Illustrative contraction / 教学性收缩本演示随观测相位增多而启发式收缩候选分布，用于解释信息量变化；它不是经过真实 cohort 校准的 Bayesian inference。
08
约束 I：逐点后验可信区间带Constraint I: Pointwise Credible Band
95% pointwise posterior credible band — not a frequentist confidence guarantee.
Terminology guardrail
L(t)=Q0.025 and U(t)=Q0.975 are pointwise posterior quantiles. Do not read them as simultaneous 95% coverage.09
每个时间点都在可信区间内，整条轨迹就一定合理吗？But Is “Inside the Band” Enough?
Pointwise plausible ≠ trajectory plausible / 逐点合理 ≠ 整条轨迹合理
Pointwise plausible≠Trajectory plausible不同 generated points 分别借用了不同 candidate trajectory 的局部合法值。
10
约束 II：整条轨迹一致性Constraint II: Whole-Trajectory Consistency
Match the generated sequence to one complete posterior-supported trajectory.
InterpretationTrajectory constraint does not force one assumed “true curve”; it asks the generated sequence to remain close to a complete trajectory supported by the patient's posterior.整轨迹约束不强迫唯一“真曲线”，而是要求生成序列靠近患者后验支持的一条完整轨迹。
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几何解释Geometric Interpretation
Band checks coordinate-wise feasibility; trajectory loss checks distance to the patient-supported kinetic set.
Band loss0.0000
Trajectory distance0.0000
StateInside box · away from supported set
Lightweight pointer orbit · arrow keys / Home reset · synthetic teaching data
Pointwise box
[L1, U1] × [L2, U2] × [L3, U3]ŷ ∈ Box → Band ≈ 0Patient-supported kinetic set
Mp = { C(t; θ(j)) }ŷ far from Mp → Trajectory > 0“Manifold” is used as geometric intuition here; it is not a claim that posterior support has been rigorously proven to be a mathematical manifold. The plotted tube is a visual guide to a finite synthetic posterior sample, not a proof of manifold structure.
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Band 与 Trajectory 交互矩阵Band vs Trajectory Interactive Matrix
Pointwise and joint losses expose different failure modes.
Trajectory Loss ↑
Band Loss →
Quadrants are teaching categories, not absolute mathematical impossibilities; interpretation depends on posterior and band construction.
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为什么不强制一条最佳拟合曲线？Why Not Force One Best-Fit Curve?
Uncertainty is information, not merely nuisance to remove.
Hard single-curve supervision
“You must follow this one trajectory.”
把 θ* 当成唯一患者真值，并强迫生成器遵循单条曲线。
Fragile under sparse observations, measurement noise, and nonlinear parameter coupling.
Uncertainty-aware posterior guidance
“These trajectories remain supported by the available patient information.”
保留当前患者信息仍支持的轨迹族，再分别施加逐点与整轨迹约束。
Uncertainty is treated as part of the information available to the model.
Does trajectory guidance choose the one true curve? / 会选择唯一真曲线吗？
No. It selects proximity to a posterior-supported explanation, not a claim of unique truth.
Why keep a band if trajectory loss exists? / 有轨迹损失后为什么保留 Band？
The band is an interpretable pointwise diagnostic and constraint; trajectory matching adds the joint consistency that the band cannot see.
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稠密到稀疏实验模拟器Dense-to-Sparse Experiment Simulator
See how phase selection changes posterior uncertainty and trajectory-family width.
15
常见误解实验室Common Misconceptions
Test the claim, then inspect the evidence / 先判断，再查看证据。
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完整拟议训练框架Full Proposed Training Framework
Multi-level temporal regularization: LDL + Band + Trajectory.
PATIENT-SPECIFIC KINETIC BRANCH
Sparse DCE observations Dp
↓
Population prior p(θ) → Posterior p(θ | Dp)
Bandpointwise plausibility
Trajectorywhole-trajectory coherence
CEKWORLD GENERATION BRANCH
Pre-contrast MRI + target τdce
↓
CEKWorld → ε̂θLDL here
↓
x̂0 → frozen differentiable VAE decoder → Î(t)
↓
ROI / kinetic measurement operator → ŷ(t)
LCEKWorld retains base diffusion + LAL + LDL + original configured terms; kinetic losses do not replace LDL.
Level 1Noise-prediction temporal regularity — LDL
Level 2Patient-specific pointwise kinetic plausibility — Band
Level 3Patient-specific whole-trajectory coherence — Trajectory
RESEARCH EXTENSION PRESENTATION