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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Generator Matching without Generators</title>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<script>
window.MathJax = {
tex: {
inlineMath: [['$', '$'], ['\\(', '\\)']],
macros: {
R: "\\mathbb{R}",
E: "\\mathbb{E}",
Var: "\\mathrm{Var}",
Prob: "\\mathbb{P}"
}
}
};
</script>
<script type="importmap">
{
"imports": {
"three": "https://cdn.jsdelivr.net/npm/three@0.185.1/build/three.module.js",
"three/addons/": "https://cdn.jsdelivr.net/npm/three@0.185.1/examples/jsm/"
}
}
</script>
<style>
:root {
/* Light theme tuned for white background */
--text-color: #222222;
--bg-color: #f5f6fa;
--slide-bg: #ffffff;
--primary-color: #0056b3;
--accent-color: #d63384;
--secondary-accent: #2e7d32;
--code-bg: #f1f3f5;
--border-color: #e0e0e0;
--nav-bg: rgba(255, 255, 255, 0.95);
}
* {
box-sizing: border-box;
margin: 0;
padding: 0;
}
html, body {
height: 100%;
overflow: hidden;
}
body {
font-family: "Crimson Pro", "Georgia", serif;
background: var(--bg-color);
color: var(--text-color);
}
/* Slideshow Container */
.slideshow-container {
position: relative;
width: 100%;
height: 100vh;
overflow: hidden;
}
.slide {
display: none;
position: absolute;
top: 0;
left: 0;
width: 100%;
height: 100%;
padding: 60px 80px 100px;
overflow-y: auto;
animation: fadeIn 0.4s ease-out;
}
.slide.active {
display: flex;
flex-direction: column;
}
@keyframes fadeIn {
from { opacity: 0; transform: translateX(20px); }
to { opacity: 1; transform: translateX(0); }
}
/* Slide Content */
.slide-content {
max-width: 1100px;
margin: 0 auto;
width: 100%;
flex: 1;
}
h1 {
font-family: "Space Grotesk", -apple-system, BlinkMacSystemFont, sans-serif;
font-size: 3rem;
font-weight: 700;
background: linear-gradient(135deg, var(--primary-color) 0%, var(--accent-color) 100%);
-webkit-background-clip: text;
-webkit-text-fill-color: transparent;
background-clip: text;
margin-bottom: 0.5rem;
text-align: center;
}
h2 {
font-family: "Space Grotesk", -apple-system, BlinkMacSystemFont, sans-serif;
font-size: 2.2rem;
font-weight: 600;
color: var(--primary-color);
margin-bottom: 1.5rem;
padding-bottom: 0.5rem;
border-bottom: 2px solid var(--border-color);
}
h3 {
font-family: "Space Grotesk", -apple-system, BlinkMacSystemFont, sans-serif;
font-size: 1.5rem;
font-weight: 500;
color: var(--secondary-accent);
margin: 1.5rem 0 1rem;
}
h4 {
font-family: "Space Grotesk", -apple-system, BlinkMacSystemFont, sans-serif;
font-size: 1.2rem;
color: var(--accent-color);
margin: 0 0 1rem;
}
.subtitle {
text-align: center;
color: #aaa;
font-size: 1.3rem;
font-style: italic;
margin-bottom: 1rem;
}
.author {
text-align: center;
color: var(--accent-color);
font-size: 1.2rem;
margin-bottom: 2rem;
}
/* Abstract/Callout Box */
.callout {
background: linear-gradient(135deg, rgba(0, 86, 179, 0.06) 0%, rgba(214, 51, 132, 0.06) 100%);
padding: 1.5rem 2rem;
border-radius: 12px;
border-left: 4px solid var(--primary-color);
margin: 1.5rem 0;
font-size: 1.1rem;
line-height: 1.7;
}
.callout strong {
color: var(--primary-color);
}
/* Lists */
ul, ol {
margin: 1rem 0 1rem 1.5rem;
font-size: 1.25rem;
line-height: 1.8;
}
li {
margin-bottom: 0.8rem;
}
li::marker {
color: var(--accent-color);
}
/* Key points */
.key-point {
background: rgba(129, 199, 132, 0.15);
border-left: 4px solid var(--secondary-accent);
padding: 1rem 1.5rem;
margin: 1.5rem 0;
border-radius: 0 8px 8px 0;
font-size: 1.15rem;
}
.key-point strong {
color: var(--secondary-accent);
}
.slide-reference {
margin: 0.9rem 0 0;
color: #59636f;
font-size: 0.84rem;
line-height: 1.45;
}
.slide-reference a {
color: var(--primary-color);
}
/* Equations */
.equation {
text-align: center;
margin: 1.5rem 0;
font-size: 1.3rem;
padding: 1rem;
background: rgba(0, 0, 0, 0.03);
border-radius: 8px;
}
/* Blockquote for process steps */
blockquote {
background: rgba(79, 195, 247, 0.08);
border-left: 4px solid var(--accent-color);
padding: 1rem 1.5rem;
margin: 1.5rem 0;
border-radius: 0 8px 8px 0;
}
blockquote ol {
margin: 0.5rem 0 0.5rem 1.5rem;
}
/* Links */
a {
color: var(--primary-color);
text-decoration: none;
border-bottom: 1px dotted var(--primary-color);
transition: all 0.2s;
}
a:hover {
color: var(--accent-color);
border-bottom-color: var(--accent-color);
}
/* Interactive Figure Container */
.interactive-figure {
background: var(--slide-bg);
border: 1px solid var(--border-color);
border-radius: 12px;
box-shadow: 0 4px 16px rgba(0, 0, 0, 0.08);
padding: 1.5rem;
text-align: center;
margin: 1rem auto;
max-width: 850px;
}
.slide-content--wide {
max-width: min(1200px, calc(100vw - 160px));
}
.interactive-figure--wide {
max-width: none;
width: 100%;
padding: 0.75rem 1rem;
}
.interactive-figure--wide .viz-svg--wide {
width: 100%;
max-width: 100%;
margin: 0 auto;
}
.marginal-svg,
.viz-svg {
display: block;
width: 100%;
max-width: 800px;
height: auto;
margin: 0 auto;
border: 1px solid var(--border-color);
border-radius: 8px;
cursor: crosshair;
font-family: "Space Grotesk", -apple-system, system-ui, sans-serif;
}
.viz-svg--wide {
max-width: 1120px;
}
.viz-svg--fm {
max-width: 900px;
}
.gm2d-figure {
max-width: none;
width: 100%;
margin: 0.35rem auto 0;
padding: 0.55rem 0.65rem 0.45rem;
}
.gm2d-controls {
justify-content: flex-start;
gap: 6px 10px;
margin: 0 0 0.45rem;
padding: 7px 9px;
min-height: 42px;
font-size: 0.76rem;
}
.gm2d-controls button {
padding: 5px 10px;
font-size: 0.76rem;
}
.gm2d-controls .gm2d-segment {
display: inline-flex;
gap: 2px;
padding: 2px;
border-radius: 7px;
background: #e8edf3;
}
.gm2d-controls .gm2d-segment button {
background: transparent;
color: #52606d;
box-shadow: none;
}
.gm2d-controls .gm2d-segment button.active {
background: #ffffff;
color: var(--primary-color);
box-shadow: 0 1px 4px rgba(36, 65, 95, 0.18);
}
.gm2d-controls label {
display: inline-flex;
align-items: center;
gap: 4px;
color: #56616d;
white-space: nowrap;
}
.gm2d-controls input[type=range] {
width: 72px;
}
.gm2d-controls output {
min-width: 28px;
color: var(--primary-color);
font-variant-numeric: tabular-nums;
}
.gm2d-controls .gm2d-toggle {
gap: 3px;
}
.gm2d-controls .gm2d-stats {
margin-left: auto;
color: #697581;
font-variant-numeric: tabular-nums;
}
.gm2d-three {
position: relative;
width: 100%;
max-width: none;
height: min(540px, 59vh);
background: linear-gradient(180deg, #fbfdff 0%, #f7f9fc 100%);
border: 1px solid var(--border-color);
border-radius: 8px;
overflow: hidden;
cursor: grab;
touch-action: none;
}
.gm2d-three:active {
cursor: grabbing;
}
.sphere-three {
height: min(450px, 50vh);
}
.gm2d-three canvas {
display: block;
width: 100%;
height: 100%;
}
.gm2d-three .gm2d-loss {
position: absolute;
left: 12px;
bottom: 12px;
width: 220px;
height: 76px;
border: 1px solid rgba(120, 136, 153, 0.28);
border-radius: 8px;
background: rgba(255, 255, 255, 0.88);
box-shadow: 0 2px 8px rgba(36, 56, 79, 0.08);
pointer-events: none;
}
.gm2d-three .gm2d-loss[hidden] {
display: none;
}
.gm2d-help {
position: absolute;
top: 10px;
right: 12px;
padding: 5px 8px;
border-radius: 6px;
background: rgba(255, 255, 255, 0.82);
color: #697887;
font: 600 0.7rem "Space Grotesk", sans-serif;
pointer-events: none;
}
.gm2d-loading {
display: grid;
place-items: center;
height: 100%;
color: #71808f;
font: 600 0.9rem "Space Grotesk", sans-serif;
}
.gm2d-controls .gm2d-sample-only[hidden] {
display: none;
}
.gm2d-lead {
margin: -0.65rem 0 0.25rem;
text-align: center;
color: #5b6570;
font-size: 0.94rem;
}
.viz-svg--sim {
cursor: crosshair;
}
.marginal-svg {
cursor: default;
}
.marginal-svg .marg-trail,
.viz-svg .viz-trail {
fill: none;
stroke-linecap: round;
stroke-linejoin: round;
shape-rendering: geometricPrecision;
vector-effect: non-scaling-stroke;
}
.marginal-svg .marg-dot,
.viz-svg .viz-dot {
shape-rendering: geometricPrecision;
}
/* Collapsible plot settings (title slide) */
.viz-settings-wrap {
position: fixed;
bottom: 72px;
right: 24px;
z-index: 1002;
}
.viz-settings-toggle {
padding: 8px 14px;
background: var(--nav-bg);
backdrop-filter: blur(10px);
border: 1px solid var(--border-color);
border-radius: 8px;
font-family: "Space Grotesk", -apple-system, sans-serif;
font-size: 0.82rem;
font-weight: 600;
color: var(--primary-color);
cursor: pointer;
box-shadow: 0 2px 12px rgba(0, 0, 0, 0.1);
transition: background 0.2s, box-shadow 0.2s;
}
.viz-settings-toggle:hover {
box-shadow: 0 4px 16px rgba(0, 0, 0, 0.14);
}
.viz-settings-panel {
display: none;
position: absolute;
bottom: calc(100% + 8px);
right: 0;
background: var(--nav-bg);
backdrop-filter: blur(10px);
border: 1px solid var(--border-color);
border-radius: 10px;
padding: 10px 14px;
font-family: "Space Grotesk", -apple-system, sans-serif;
font-size: 0.78rem;
color: var(--text-color);
box-shadow: 0 4px 16px rgba(0, 0, 0, 0.12);
width: 220px;
}
.viz-settings-wrap.open .viz-settings-panel {
display: block;
}
.viz-settings-panel h4 {
margin: 0 0 8px;
font-size: 0.82rem;
font-weight: 600;
color: var(--primary-color);
}
.viz-settings-panel label {
display: flex;
flex-direction: column;
gap: 3px;
margin-bottom: 8px;
color: var(--text-color);
font-size: 0.75rem;
}
.viz-settings-panel select,
.viz-settings-panel input[type=range] {
width: 100%;
}
.viz-settings-panel .viz-val {
font-family: monospace;
font-size: 0.72rem;
color: #888;
text-align: right;
}
.controls {
margin-top: 15px;
font-family: "Space Grotesk", -apple-system, sans-serif;
font-size: 0.9rem;
display: flex;
justify-content: center;
align-items: center;
gap: 15px;
flex-wrap: wrap;
padding: 12px;
background: #f8f9fa;
border-radius: 8px;
}
button {
padding: 8px 16px;
background: linear-gradient(135deg, var(--primary-color) 0%, #29b6f6 100%);
color: #1a1a2e;
font-weight: 600;
border: none;
border-radius: 6px;
cursor: pointer;
transition: all 0.2s;
font-size: 0.9rem;
font-family: "Space Grotesk", -apple-system, sans-serif;
}
button:hover {
transform: translateY(-2px);
box-shadow: 0 4px 12px rgba(79, 195, 247, 0.4);
}
button.secondary {
background: linear-gradient(135deg, #546e7a 0%, #455a64 100%);
color: white;
}
button.active {
background: linear-gradient(135deg, var(--accent-color) 0%, #ec407a 100%);
}
.controls.sim-controls {
gap: 8px;
}
.controls.sim-controls .sim-mode-btn {
padding: 6px 12px;
font-size: 0.82rem;
background: #e8ecf0;
color: var(--text-color);
}
.controls.sim-controls .sim-mode-btn.active {
background: linear-gradient(135deg, var(--primary-color) 0%, #29b6f6 100%);
color: #1a1a2e;
}
.controls .diff-vp-mode-btn.active {
background: linear-gradient(135deg, var(--primary-color) 0%, #29b6f6 100%);
color: #1a1a2e;
}
input[type=range] {
vertical-align: middle;
accent-color: var(--primary-color);
}
input[type=number] {
width: 55px;
padding: 6px;
background: var(--code-bg);
border: 1px solid var(--border-color);
border-radius: 4px;
color: var(--text-color);
font-family: inherit;
}
label {
color: #bbb;
}
.caption {
font-size: 0.9rem;
color: #999;
margin-top: 1rem;
font-family: "Space Grotesk", -apple-system, sans-serif;
line-height: 1.5;
}
/* Navigation */
.nav-bar {
position: fixed;
bottom: 0;
left: 0;
right: 0;
background: var(--nav-bg);
backdrop-filter: blur(10px);
padding: 15px 30px;
display: flex;
justify-content: space-between;
align-items: center;
border-top: 1px solid var(--border-color);
z-index: 1000;
}
.nav-btn {
padding: 10px 24px;
font-size: 1rem;
min-width: 120px;
}
.nav-btn:disabled {
opacity: 0.4;
cursor: not-allowed;
transform: none !important;
box-shadow: none !important;
}
.slide-counter {
font-family: "Space Grotesk", monospace;
font-size: 1rem;
color: #888;
}
.slide-counter .current {
color: var(--primary-color);
font-weight: 600;
}
/* Progress bar */
.progress-bar {
position: fixed;
top: 0;
left: 0;
height: 3px;
background: linear-gradient(90deg, var(--primary-color), var(--accent-color));
transition: width 0.3s ease;
z-index: 1001;
}
/* Image styling */
.slide img {
max-width: 100%;
border-radius: 8px;
margin: 1rem auto;
display: block;
}
/* Two column layout */
.two-col {
display: grid;
grid-template-columns: 1fr 1fr;
gap: 2rem;
margin: 1rem 0;
}
/* Opening motivation slides */
.motivation-lead {
max-width: 900px;
margin: -0.35rem auto 0.7rem;
text-align: center;
font-family: "Space Grotesk", -apple-system, sans-serif;
font-size: 1.2rem;
color: #555;
}
.motivation-figure {
max-width: 1040px;
padding: 0.75rem;
margin-top: 0.5rem;
}
.motivation-figure--ar {
max-width: 960px;
}
.motivation-svg {
max-width: 1000px;
cursor: default;
border: none;
background: linear-gradient(145deg, #fbfcff 0%, #f4f7fb 100%);
}
.motivation-equation {
max-width: 900px;
margin: 0.75rem auto;
padding: 0.55rem 1rem;
font-size: 1.15rem;
}
.motivation-question {
max-width: 900px;
margin: 0.7rem auto 0;
padding: 0.75rem 1.2rem;
text-align: center;
font-family: "Space Grotesk", -apple-system, sans-serif;
font-size: 1.1rem;
color: var(--secondary-accent);
background: rgba(46, 125, 50, 0.08);
border-radius: 10px;
}
.history-timeline {
position: relative;
max-width: 1020px;
margin: 0.2rem auto 0;
padding: 0.15rem 0;
}
.history-timeline::before {
content: "";
position: absolute;
top: 1rem;
bottom: 1rem;
left: 174px;
width: 3px;
border-radius: 2px;
background: linear-gradient(180deg, #d63384 0%, #0056b3 58%, #2e7d32 100%);
}
.history-item {
position: relative;
display: grid;
grid-template-columns: 150px 48px minmax(0, 1fr);
align-items: center;
min-height: 68px;
}
.history-date {
text-align: right;
font-family: "Space Grotesk", -apple-system, sans-serif;
font-size: 0.92rem;
font-weight: 600;
color: #667583;
font-variant-numeric: tabular-nums;
}
.history-dot {
position: relative;
z-index: 1;
justify-self: center;
width: 15px;
height: 15px;
border: 3px solid #fff;
border-radius: 50%;
background: var(--primary-color);
box-shadow: 0 0 0 2px currentColor;
color: var(--primary-color);
}
.history-item--diffusion .history-dot { background: var(--accent-color); color: var(--accent-color); }
.history-item--gm .history-dot { background: var(--secondary-accent); color: var(--secondary-accent); }
.history-cite {
padding: 0.55rem 0.8rem;
border: 1px solid #e5eaf0;
border-radius: 9px;
background: rgba(250, 252, 255, 0.92);
line-height: 1.18;
}
.history-cite a {
color: var(--text-color);
font-size: 1rem;
font-weight: 600;
text-decoration: none;
}
.history-cite a:hover { color: var(--primary-color); text-decoration: underline; }
.history-authors {
margin-top: 0.18rem;
font-family: "Space Grotesk", -apple-system, sans-serif;
font-size: 0.76rem;
color: #74808c;
}
.masked-process {
display: grid;
grid-template-columns: 1fr auto 1fr;
align-items: center;
gap: 1.1rem;
max-width: 850px;
margin: 0.6rem auto 1rem;
}
.masked-state-card {
padding: 1rem;
text-align: center;
border: 1px solid #dfe6ee;
border-radius: 12px;
background: #fafcff;
}
.masked-token-row {
display: flex;
justify-content: center;
gap: 0.45rem;
margin: 0.35rem 0;
}
.masked-token {
display: inline-grid;
place-items: center;
width: 54px;
height: 54px;
border-radius: 9px;
background: #e7edf4;
color: #647383;
font-family: "Space Grotesk", sans-serif;
font-size: 1.35rem;
font-weight: 700;
}
.masked-token--known { background: #e5f2ff; color: var(--primary-color); }
.masked-arrow { font-family: "Space Grotesk", sans-serif; font-size: 1.4rem; color: var(--accent-color); }
.masked-equations {
display: grid;
grid-template-columns: 1fr 1fr;
gap: 1rem;
margin-top: 0.6rem;
}
.masked-equations .equation { margin: 0; padding: 0.75rem 0.9rem; font-size: 0.96rem; }
.parity-workbench {
display: grid;
grid-template-columns: 0.84fr 1.16fr;
gap: 0.9rem;
margin-top: 0.65rem;
}
.parity-panel {
min-height: 382px;
padding: 0.9rem;
border: 1px solid #dfe6ee;
border-radius: 11px;
background: #fbfcff;
}
.parity-panel h3 { margin: 0 0 0.3rem; font-size: 1.05rem; }
.parity-targets {
display: grid;
grid-template-columns: 1fr 1fr;
gap: 0.45rem;
margin: 0.55rem 0 0.6rem;
}
.parity-code {
padding: 0.45rem;
text-align: center;
border-radius: 7px;
background: #eaf3ff;
color: var(--primary-color);
font: 700 1.05rem "Space Grotesk", monospace;
letter-spacing: 0.16em;
}
.parity-mini { font: 0.76rem/1.35 "Space Grotesk", sans-serif; color: #74808c; }
.parity-loss-plot, .parity-histogram { width: 100%; display: block; overflow: visible; }
.parity-loss-plot { height: 190px; margin-top: 0.15rem; }
.parity-histogram { height: 140px; margin-top: 0.05rem; }
.parity-axis { stroke: #aab5c1; stroke-width: 1; }
.parity-grid { stroke: #e5eaf0; stroke-width: 1; }
.parity-loss-line { fill: none; stroke: #0067c5; stroke-width: 3; stroke-linecap: round; stroke-linejoin: round; }
.parity-svg-label { fill: #73808e; font: 12px "Space Grotesk", sans-serif; }
.parity-time-head, .parity-lane {
display: grid;
grid-template-columns: repeat(4, 1fr);
gap: 0.35rem;
align-items: center;
}
.parity-time-head { margin: 0.4rem 0 0.25rem; color: #778594; font: 0.68rem "Space Grotesk", sans-serif; text-align: center; }
.parity-lanes { display: grid; gap: 0.22rem; min-height: 126px; }
.parity-lane-state {
padding: 0.32rem 0.2rem;
border-radius: 6px;
background: #edf2f7;
color: #8894a0;
text-align: center;
font: 700 0.86rem "Space Grotesk", monospace;
letter-spacing: 0.1em;
opacity: 0.28;
}
.parity-lane-state--seen { opacity: 1; background: #e8f2ff; color: var(--primary-color); }
.parity-lane-state--done { background: #e7f6ec; color: #19733a; }
.parity-sample-rule { border: 0; border-top: 1px solid #e2e8ef; margin: 0.45rem 0 0.3rem; }
.parity-hist-title { display: flex; justify-content: space-between; align-items: baseline; }
.parity-legend { display: flex; gap: 0.8rem; font: 0.7rem "Space Grotesk", sans-serif; color: #74808c; }
.parity-legend i { display: inline-block; width: 10px; height: 10px; margin-right: 0.25rem; border-radius: 2px; vertical-align: -1px; }
.parity-controls { display: flex; align-items: center; gap: 0.55rem; margin-top: 0.65rem; }
.parity-stats { margin-left: auto; font: 0.78rem "Space Grotesk", sans-serif; color: #6f7d8b; }
/* SVG figures */
.svg-figure {
background: var(--slide-bg);
border: 1px solid var(--border-color);
border-radius: 12px;
padding: 1.5rem;
margin: 1rem 0;
}
.svg-figure img {
max-width: 100%;
margin: 0 auto;
}
.svg-figure .caption {
text-align: center;
margin-top: 1rem;
}
/* Title slide special - only style when active */
.slide.title-slide.active {
justify-content: center;
align-items: center;
text-align: center;
}
.title-slide h1 {
font-size: 4rem;
margin-bottom: 1rem;
}
/* Compact list for slides */
.compact-list {
font-size: 1.15rem;
}
.compact-list li {
margin-bottom: 0.5rem;
}
/* Keyboard hint */
.keyboard-hint {
position: fixed;
bottom: 80px;
right: 30px;
font-size: 0.8rem;
color: #666;
font-family: "Space Grotesk", monospace;
}
kbd {
background: var(--code-bg);
border: 1px solid var(--border-color);
border-radius: 4px;
padding: 2px 6px;
font-family: inherit;
}
/* Slide list sidebar */
.slide-list-toggle {
position: fixed;
top: 14px;
left: 14px;
z-index: 1002;
padding: 8px 14px;
font-family: "Space Grotesk", -apple-system, sans-serif;
font-size: 0.85rem;