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QAFD-RAG
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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>QAFD-RAG: Query-Aware Flow Diffusion for Graph-Based RAG</title>
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      --white: #ffffff; --radius: 10px; --radius-lg: 16px;
    }
    * { margin: 0; padding: 0; box-sizing: border-box; }
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      animation: logoFadeIn 1s ease-out;
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    @keyframes logoFadeIn { from { opacity:0; transform: scale(0.9) translateY(10px); } to { opacity:1; transform: scale(1) translateY(0); } }
    @keyframes waterFlow { 0% { stroke-dashoffset: var(--len); opacity:0.85; } 100% { stroke-dashoffset:0; opacity:0.85; } }
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          <circle cx="55" cy="155" r="2.2"/><circle cx="95" cy="55" r="2.5"/><circle cx="75" cy="95" r="2.2"/>
          <circle cx="110" cy="120" r="2"/><circle cx="130" cy="40" r="2.2"/><circle cx="85" cy="180" r="2"/>
          <circle cx="65" cy="220" r="2"/><circle cx="120" cy="200" r="2.2"/><circle cx="100" cy="240" r="2"/>
          <circle cx="130" cy="265" r="2"/><circle cx="170" cy="18" r="2.2"/><circle cx="220" cy="12" r="2.2"/>
          <circle cx="275" cy="18" r="2"/><circle cx="320" cy="12" r="2"/><circle cx="350" cy="22" r="2.2"/>
          <circle cx="385" cy="15" r="2"/><circle cx="410" cy="40" r="2"/><circle cx="405" cy="85" r="2.2"/>
          <circle cx="410" cy="135" r="2"/><circle cx="400" cy="180" r="2.2"/><circle cx="408" cy="230" r="2"/>
          <circle cx="390" cy="260" r="2"/><circle cx="370" cy="60" r="2.5"/><circle cx="355" cy="100" r="2.5"/>
          <circle cx="375" cy="140" r="2.2"/><circle cx="350" cy="175" r="2.2"/><circle cx="370" cy="215" r="2"/>
          <circle cx="320" cy="200" r="2.2"/><circle cx="340" cy="240" r="2"/><circle cx="308" cy="260" r="2"/>
          <circle cx="290" cy="220" r="2"/><circle cx="260" cy="255" r="2"/><circle cx="175" cy="270" r="2"/>
          <circle cx="220" cy="265" r="2"/><circle cx="270" cy="45" r="2"/><circle cx="210" cy="60" r="2"/>
          <circle cx="325" cy="118" r="3"/><circle cx="305" cy="68" r="2.8"/>
          <circle cx="262" cy="148" r="2.8"/><circle cx="262" cy="92" r="2.8"/>
          <circle cx="210" cy="175" r="2.5"/><circle cx="158" cy="92" r="2.5"/>
          <circle cx="158" cy="148" r="2.2"/><circle cx="112" cy="62" r="2.2"/>
          <circle cx="92" cy="35" r="2"/><circle cx="210" cy="25" r="2"/>
          <circle cx="210" cy="218" r="2.2"/><circle cx="190" cy="250" r="2"/>
          <circle cx="335" cy="165" r="2"/><circle cx="118" cy="178" r="2"/>
          <circle cx="322" cy="35" r="2"/>
        </g>

        <!--
          PHASE 1: BUILD — water shoots from source, pipe+node appear where it lands
          PHASE 2: LOOP — after build, continuous flow from source outward
          
          Each element uses <animate> with begin= for precise timing.
          Pipe: starts invisible, fades in when water arrives
          Node: starts invisible, pops when pipe reaches it
          Water: draws from source outward using stroke-dashoffset
        -->

        <!-- ======= SOURCE (0s) ======= -->
        <circle cx="325" cy="118" r="20" fill="url(#srcGl)" filter="url(#sB)" opacity="0"><animate attributeName="opacity" to="1" dur="0.4s" begin="0.2s" fill="freeze"/></circle>
        <g filter="url(#sG)" opacity="0"><animate attributeName="opacity" to="1" dur="0.4s" begin="0.2s" fill="freeze"/>
          <circle cx="325" cy="118" r="14" fill="url(#src)"/><circle cx="325" cy="118" r="14" fill="url(#srcSp)"/>
          <ellipse cx="320" cy="111" rx="4.5" ry="3" fill="#FFF" opacity="0.5"/>
        </g>

        <!-- ======= HOP 1: Source→G(305,68) and Source→D(262,148) ======= -->
        <!-- Water Source→G -->
        <path d="M325,118 C318,100 312,85 305,68" fill="none" stroke="#7DD3FC" stroke-width="5.5" stroke-linecap="round" stroke-dasharray="55" stroke-dashoffset="55" opacity="0"><animate attributeName="stroke-dashoffset" to="0" dur="0.6s" begin="0.5s" fill="freeze"/><animate attributeName="opacity" to="0.85" dur="0.1s" begin="0.5s" fill="freeze"/></path>
        <!-- Pipe Source→G fades in -->
        <path d="M305,68 C312,85 318,100 325,118" fill="none" stroke="#172554" stroke-width="10" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.9" dur="0.3s" begin="0.7s" fill="freeze"/></path>
        <path d="M305,68 C312,85 318,100 325,118" fill="none" stroke="url(#pSh)" stroke-width="4.5" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.55" dur="0.3s" begin="0.75s" fill="freeze"/></path>
        <!-- G node pops -->
        <g filter="url(#nG)" opacity="0"><animate attributeName="opacity" to="1" dur="0.3s" begin="0.85s" fill="freeze"/>
          <circle cx="305" cy="68" r="9" fill="url(#s1)"/><circle cx="305" cy="68" r="9" fill="url(#s1sp)"/>
        </g>

        <!-- Water Source→D -->
        <path d="M325,118 C305,128 282,138 262,148" fill="none" stroke="#7DD3FC" stroke-width="5" stroke-linecap="round" stroke-dasharray="75" stroke-dashoffset="75" opacity="0"><animate attributeName="stroke-dashoffset" to="0" dur="0.7s" begin="0.55s" fill="freeze"/><animate attributeName="opacity" to="0.85" dur="0.1s" begin="0.55s" fill="freeze"/></path>
        <path d="M262,148 C282,138 305,128 325,118" fill="none" stroke="#172554" stroke-width="9.5" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.88" dur="0.3s" begin="0.8s" fill="freeze"/></path>
        <path d="M262,148 C282,138 305,128 325,118" fill="none" stroke="url(#pSh)" stroke-width="4.2" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.52" dur="0.3s" begin="0.85s" fill="freeze"/></path>
        <g filter="url(#nG)" opacity="0"><animate attributeName="opacity" to="1" dur="0.3s" begin="0.95s" fill="freeze"/>
          <circle cx="262" cy="148" r="10" fill="url(#s1)"/><circle cx="262" cy="148" r="10" fill="url(#s1sp)"/>
        </g>

        <!-- ======= HOP 2: G→C and D→C (converging) ======= -->
        <path d="M305,68 C290,72 275,82 262,92" fill="none" stroke="#7DD3FC" stroke-width="5" stroke-linecap="round" stroke-dasharray="55" stroke-dashoffset="55" opacity="0"><animate attributeName="stroke-dashoffset" to="0" dur="0.6s" begin="1.0s" fill="freeze"/><animate attributeName="opacity" to="0.85" dur="0.1s" begin="1.0s" fill="freeze"/></path>
        <path d="M262,92 C275,82 290,72 305,68" fill="none" stroke="#172554" stroke-width="9.5" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.86" dur="0.3s" begin="1.2s" fill="freeze"/></path>
        <path d="M262,92 C275,82 290,72 305,68" fill="none" stroke="url(#pSh)" stroke-width="4.2" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.5" dur="0.3s" begin="1.25s" fill="freeze"/></path>

        <path d="M262,148 C262,130 262,110 262,92" fill="none" stroke="#7DD3FC" stroke-width="5" stroke-linecap="round" stroke-dasharray="56" stroke-dashoffset="56" opacity="0"><animate attributeName="stroke-dashoffset" to="0" dur="0.55s" begin="1.05s" fill="freeze"/><animate attributeName="opacity" to="0.85" dur="0.1s" begin="1.05s" fill="freeze"/></path>
        <path d="M262,92 C262,110 262,130 262,148" fill="none" stroke="#172554" stroke-width="9.5" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.84" dur="0.3s" begin="1.25s" fill="freeze"/></path>
        <path d="M262,92 C262,110 262,130 262,148" fill="none" stroke="url(#pSh)" stroke-width="4.2" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.5" dur="0.3s" begin="1.3s" fill="freeze"/></path>

        <g filter="url(#nG)" opacity="0"><animate attributeName="opacity" to="1" dur="0.3s" begin="1.35s" fill="freeze"/>
          <circle cx="262" cy="92" r="10" fill="url(#s1)"/><circle cx="262" cy="92" r="10" fill="url(#s1sp)"/>
        </g>

        <!-- ======= HOP 3: C→B→A (6-ring top) and D→E→F (6-ring bottom) ======= -->
        <!-- C→B -->
        <path d="M262,92 C245,78 228,68 210,60" fill="none" stroke="#93C5FD" stroke-width="4.2" stroke-linecap="round" stroke-dasharray="62" stroke-dashoffset="62" opacity="0"><animate attributeName="stroke-dashoffset" to="0" dur="0.6s" begin="1.5s" fill="freeze"/><animate attributeName="opacity" to="0.85" dur="0.1s" begin="1.5s" fill="freeze"/></path>
        <path d="M210,60 C228,68 245,78 262,92" fill="none" stroke="#1E3A8A" stroke-width="8.5" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.72" dur="0.3s" begin="1.7s" fill="freeze"/></path>
        <path d="M210,60 C228,68 245,78 262,92" fill="none" stroke="url(#pSh)" stroke-width="3.8" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.45" dur="0.3s" begin="1.75s" fill="freeze"/></path>
        <g filter="url(#nG)" opacity="0"><animate attributeName="opacity" to="1" dur="0.3s" begin="1.85s" fill="freeze"/>
          <circle cx="210" cy="60" r="9" fill="url(#s1)"/><circle cx="210" cy="60" r="9" fill="url(#s1sp)"/>
        </g>

        <!-- B→A -->
        <path d="M210,60 C192,68 175,80 158,92" fill="none" stroke="#93C5FD" stroke-width="3.8" stroke-linecap="round" stroke-dasharray="65" stroke-dashoffset="65" opacity="0"><animate attributeName="stroke-dashoffset" to="0" dur="0.6s" begin="1.9s" fill="freeze"/><animate attributeName="opacity" to="0.85" dur="0.1s" begin="1.9s" fill="freeze"/></path>
        <path d="M158,92 C175,80 192,68 210,60" fill="none" stroke="#1E3A8A" stroke-width="8" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.7" dur="0.3s" begin="2.1s" fill="freeze"/></path>
        <path d="M158,92 C175,80 192,68 210,60" fill="none" stroke="url(#pSh)" stroke-width="3.5" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.45" dur="0.3s" begin="2.15s" fill="freeze"/></path>
        <g filter="url(#nG)" opacity="0"><animate attributeName="opacity" to="1" dur="0.3s" begin="2.25s" fill="freeze"/>
          <circle cx="158" cy="92" r="9" fill="url(#s1)"/><circle cx="158" cy="92" r="9" fill="url(#s1sp)"/>
        </g>

        <!-- D→E -->
        <path d="M262,148 C245,158 228,168 210,175" fill="none" stroke="#93C5FD" stroke-width="3.8" stroke-linecap="round" stroke-dasharray="62" stroke-dashoffset="62" opacity="0"><animate attributeName="stroke-dashoffset" to="0" dur="0.6s" begin="1.5s" fill="freeze"/><animate attributeName="opacity" to="0.85" dur="0.1s" begin="1.5s" fill="freeze"/></path>
        <path d="M210,175 C228,168 245,158 262,148" fill="none" stroke="#1E3A8A" stroke-width="7.5" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.68" dur="0.3s" begin="1.7s" fill="freeze"/></path>
        <path d="M210,175 C228,168 245,158 262,148" fill="none" stroke="url(#pSh)" stroke-width="3.2" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.42" dur="0.3s" begin="1.75s" fill="freeze"/></path>
        <g filter="url(#nG)" opacity="0"><animate attributeName="opacity" to="1" dur="0.3s" begin="1.85s" fill="freeze"/>
          <circle cx="210" cy="175" r="8" fill="url(#m1)"/><circle cx="210" cy="175" r="8" fill="url(#m1sp)"/>
        </g>

        <!-- E→F -->
        <path d="M210,175 C192,168 175,158 158,148" fill="none" stroke="#BFDBFE" stroke-width="2.8" stroke-linecap="round" stroke-dasharray="65" stroke-dashoffset="65" opacity="0"><animate attributeName="stroke-dashoffset" to="0" dur="0.6s" begin="1.9s" fill="freeze"/><animate attributeName="opacity" to="0.85" dur="0.1s" begin="1.9s" fill="freeze"/></path>
        <path d="M158,148 C175,158 192,168 210,175" fill="none" stroke="#1D4ED8" stroke-width="5.5" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.5" dur="0.3s" begin="2.1s" fill="freeze"/></path>
        <g filter="url(#nG)" opacity="0"><animate attributeName="opacity" to="1" dur="0.3s" begin="2.25s" fill="freeze"/>
          <circle cx="158" cy="148" r="7" fill="url(#m1)"/><circle cx="158" cy="148" r="7" fill="url(#m1sp)"/>
        </g>

        <!-- F→A ring close -->
        <path d="M158,148 C158,130 158,112 158,92" fill="none" stroke="#BFDBFE" stroke-width="2.2" stroke-linecap="round" stroke-dasharray="56" stroke-dashoffset="56" opacity="0"><animate attributeName="stroke-dashoffset" to="0" dur="0.5s" begin="2.3s" fill="freeze"/><animate attributeName="opacity" to="0.85" dur="0.1s" begin="2.3s" fill="freeze"/></path>
        <path d="M158,92 C158,112 158,130 158,148" fill="none" stroke="#1D4ED8" stroke-width="5" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.48" dur="0.3s" begin="2.5s" fill="freeze"/></path>

        <!-- ======= HOP 4: BRANCHES ======= -->
        <!-- A→M1 -->
        <path d="M158,92 C142,80 128,70 112,62" fill="none" stroke="#93C5FD" stroke-width="3.2" stroke-linecap="round" stroke-dasharray="52" stroke-dashoffset="52" opacity="0"><animate attributeName="stroke-dashoffset" to="0" dur="0.5s" begin="2.4s" fill="freeze"/><animate attributeName="opacity" to="0.85" dur="0.1s" begin="2.4s" fill="freeze"/></path>
        <path d="M112,62 C128,70 142,80 158,92" fill="none" stroke="#1E3A8A" stroke-width="6.5" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.58" dur="0.3s" begin="2.55s" fill="freeze"/></path>
        <path d="M112,62 C128,70 142,80 158,92" fill="none" stroke="url(#pSh)" stroke-width="2.8" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.38" dur="0.3s" begin="2.6s" fill="freeze"/></path>
        <g filter="url(#nG)" opacity="0"><animate attributeName="opacity" to="1" dur="0.3s" begin="2.7s" fill="freeze"/>
          <circle cx="112" cy="62" r="7.5" fill="url(#m1)"/><circle cx="112" cy="62" r="7.5" fill="url(#m1sp)"/>
        </g>
        <!-- M1→leaf -->
        <path d="M112,62 C104,52 98,42 92,35" fill="none" stroke="#DBEAFE" stroke-width="1.5" stroke-linecap="round" stroke-dasharray="35" stroke-dashoffset="35" opacity="0"><animate attributeName="stroke-dashoffset" to="0" dur="0.4s" begin="2.8s" fill="freeze"/><animate attributeName="opacity" to="0.85" dur="0.1s" begin="2.8s" fill="freeze"/></path>
        <path d="M92,35 C98,42 104,52 112,62" fill="none" stroke="#3B82F6" stroke-width="2.8" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.25" dur="0.3s" begin="2.95s" fill="freeze"/></path>
        <circle cx="92" cy="35" r="3" fill="url(#lf)" opacity="0"><animate attributeName="opacity" to="1" dur="0.3s" begin="3.05s" fill="freeze"/></circle>

        <!-- B→M2 up -->
        <path d="M210,60 C210,48 210,35 210,25" fill="none" stroke="#BFDBFE" stroke-width="2" stroke-linecap="round" stroke-dasharray="35" stroke-dashoffset="35" opacity="0"><animate attributeName="stroke-dashoffset" to="0" dur="0.4s" begin="2.1s" fill="freeze"/><animate attributeName="opacity" to="0.85" dur="0.1s" begin="2.1s" fill="freeze"/></path>
        <path d="M210,25 C210,35 210,48 210,60" fill="none" stroke="#2563EB" stroke-width="4" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.35" dur="0.3s" begin="2.25s" fill="freeze"/></path>
        <circle cx="210" cy="25" r="5" fill="url(#w1)" opacity="0"><animate attributeName="opacity" to="1" dur="0.3s" begin="2.35s" fill="freeze"/></circle>

        <!-- E→M3 down -->
        <path d="M210,175 C210,190 210,205 210,218" fill="none" stroke="#BFDBFE" stroke-width="2" stroke-linecap="round" stroke-dasharray="43" stroke-dashoffset="43" opacity="0"><animate attributeName="stroke-dashoffset" to="0" dur="0.4s" begin="2.1s" fill="freeze"/><animate attributeName="opacity" to="0.85" dur="0.1s" begin="2.1s" fill="freeze"/></path>
        <path d="M210,218 C210,205 210,190 210,175" fill="none" stroke="#2563EB" stroke-width="4" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.38" dur="0.3s" begin="2.25s" fill="freeze"/></path>
        <circle cx="210" cy="218" r="5.5" fill="url(#w1)" opacity="0"><animate attributeName="opacity" to="1" dur="0.3s" begin="2.35s" fill="freeze"/></circle>
        <!-- M3→leaf -->
        <path d="M210,218 C202,232 196,242 190,250" fill="none" stroke="#DBEAFE" stroke-width="1.3" stroke-linecap="round" stroke-dasharray="38" stroke-dashoffset="38" opacity="0"><animate attributeName="stroke-dashoffset" to="0" dur="0.4s" begin="2.5s" fill="freeze"/><animate attributeName="opacity" to="0.85" dur="0.1s" begin="2.5s" fill="freeze"/></path>
        <path d="M190,250 C196,242 202,232 210,218" fill="none" stroke="#93C5FD" stroke-width="1.8" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.16" dur="0.3s" begin="2.65s" fill="freeze"/></path>
        <circle cx="190" cy="250" r="2.5" fill="url(#lf)" opacity="0"><animate attributeName="opacity" to="1" dur="0.3s" begin="2.75s" fill="freeze"/></circle>

        <!-- Source→ext -->
        <path d="M325,118 C328,132 332,150 335,165" fill="none" stroke="#BFDBFE" stroke-width="1.8" stroke-linecap="round" stroke-dasharray="50" stroke-dashoffset="50" opacity="0"><animate attributeName="stroke-dashoffset" to="0" dur="0.5s" begin="2.0s" fill="freeze"/><animate attributeName="opacity" to="0.85" dur="0.1s" begin="2.0s" fill="freeze"/></path>
        <path d="M335,165 C332,150 328,132 325,118" fill="none" stroke="#2563EB" stroke-width="3.2" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.28" dur="0.3s" begin="2.15s" fill="freeze"/></path>
        <circle cx="335" cy="165" r="4" fill="url(#w1)" opacity="0"><animate attributeName="opacity" to="1" dur="0.3s" begin="2.3s" fill="freeze"/></circle>

        <!-- STARVED -->
        <path d="M158,148 C142,158 130,168 118,178" fill="none" stroke="#DBEAFE" stroke-width="1" stroke-linecap="round" stroke-dasharray="45" stroke-dashoffset="45" opacity="0"><animate attributeName="stroke-dashoffset" to="0" dur="0.7s" begin="3.0s" fill="freeze"/><animate attributeName="opacity" to="0.85" dur="0.1s" begin="3.0s" fill="freeze"/></path>
        <path d="M118,178 C130,168 142,158 158,148" fill="none" stroke="#60A5FA" stroke-width="2" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.13" dur="0.3s" begin="3.2s" fill="freeze"/></path>
        <circle cx="118" cy="178" r="3.5" fill="url(#st1)" opacity="0"><animate attributeName="opacity" to="1" dur="0.3s" begin="3.3s" fill="freeze"/></circle>

        <path d="M305,68 C310,55 316,42 322,35" fill="none" stroke="#DBEAFE" stroke-width="1" stroke-linecap="round" stroke-dasharray="40" stroke-dashoffset="40" opacity="0"><animate attributeName="stroke-dashoffset" to="0" dur="0.7s" begin="3.1s" fill="freeze"/><animate attributeName="opacity" to="0.85" dur="0.1s" begin="3.1s" fill="freeze"/></path>
        <path d="M322,35 C316,42 310,55 305,68" fill="none" stroke="#60A5FA" stroke-width="2.5" stroke-linecap="round" opacity="0"><animate attributeName="opacity" to="0.18" dur="0.3s" begin="3.3s" fill="freeze"/></path>
        <circle cx="322" cy="35" r="3.5" fill="url(#st1)" opacity="0"><animate attributeName="opacity" to="1" dur="0.3s" begin="3.4s" fill="freeze"/></circle>

        <!-- ======= PHASE 2: CONTINUOUS WATER LOOP from source outward (4s+) ======= -->
        <g fill="none" stroke-linecap="round" opacity="0">
          <animate attributeName="opacity" to="1" dur="0.5s" begin="4s" fill="freeze"/>
          <!-- 5-ring -->
          <path d="M325,118 C318,100 312,85 305,68" stroke="#7DD3FC" stroke-width="5.5" stroke-dasharray="12 8"><animate attributeName="stroke-dashoffset" values="0;-40" dur="1s" begin="4s" repeatCount="indefinite"/></path>
          <path d="M325,118 C305,128 282,138 262,148" stroke="#7DD3FC" stroke-width="5" stroke-dasharray="12 8"><animate attributeName="stroke-dashoffset" values="0;-40" dur="1.2s" begin="4s" repeatCount="indefinite"/></path>
          <path d="M305,68 C290,72 275,82 262,92" stroke="#7DD3FC" stroke-width="5" stroke-dasharray="12 8"><animate attributeName="stroke-dashoffset" values="0;-40" dur="1.1s" begin="4s" repeatCount="indefinite"/></path>
          <path d="M262,148 C262,130 262,110 262,92" stroke="#7DD3FC" stroke-width="5" stroke-dasharray="12 8"><animate attributeName="stroke-dashoffset" values="0;-40" dur="1s" begin="4s" repeatCount="indefinite"/></path>
          <!-- 6-ring top (outward from C) -->
          <path d="M262,92 C245,78 228,68 210,60" stroke="#93C5FD" stroke-width="4" stroke-dasharray="10 8"><animate attributeName="stroke-dashoffset" values="0;-36" dur="1.4s" begin="4s" repeatCount="indefinite"/></path>
          <path d="M210,60 C192,68 175,80 158,92" stroke="#93C5FD" stroke-width="3.8" stroke-dasharray="10 8"><animate attributeName="stroke-dashoffset" values="0;-36" dur="1.5s" begin="4s" repeatCount="indefinite"/></path>
          <!-- 6-ring bottom (outward from D) -->
          <path d="M262,148 C245,158 228,168 210,175" stroke="#93C5FD" stroke-width="3.5" stroke-dasharray="10 8"><animate attributeName="stroke-dashoffset" values="0;-36" dur="1.3s" begin="4s" repeatCount="indefinite"/></path>
          <path d="M210,175 C192,168 175,158 158,148" stroke="#BFDBFE" stroke-width="2.5" stroke-dasharray="8 8"><animate attributeName="stroke-dashoffset" values="0;-32" dur="1.6s" begin="4s" repeatCount="indefinite"/></path>
          <path d="M158,148 C158,130 158,112 158,92" stroke="#BFDBFE" stroke-width="2" stroke-dasharray="8 8"><animate attributeName="stroke-dashoffset" values="0;-32" dur="1.8s" begin="4s" repeatCount="indefinite"/></path>
          <!-- Branches (outward) -->
          <path d="M158,92 C142,80 128,70 112,62" stroke="#93C5FD" stroke-width="3" stroke-dasharray="8 7"><animate attributeName="stroke-dashoffset" values="0;-30" dur="1.4s" begin="4s" repeatCount="indefinite"/></path>
          <path d="M210,60 C210,48 210,35 210,25" stroke="#BFDBFE" stroke-width="2" stroke-dasharray="6 7"><animate attributeName="stroke-dashoffset" values="0;-26" dur="1.6s" begin="4s" repeatCount="indefinite"/></path>
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    <h1 style="font-size:2.8rem;font-weight:700;letter-spacing:-1px;margin-bottom:24px;color:var(--navy-900);animation:fadeUp 0.6s ease-out 0.3s both;">QAFD-RAG</h1>
    <div class="btn-group">
      <a class="btn btn-primary" href="https://openreview.net/pdf?id=n28wnc2QTc"><svg viewBox="0 0 24 24" fill="currentColor"><path d="M14 2H6a2 2 0 0 0-2 2v16a2 2 0 0 0 2 2h12a2 2 0 0 0 2-2V8l-6-6zm-1 2l5 5h-5V4zM6 20V4h5v7h7v9H6z"/></svg> Paper</a>
      <a class="btn btn-outline" href="https://github.com/Tarzanagh/QAFD-RAG"><svg viewBox="0 0 24 24" fill="currentColor"><path d="M12 0C5.37 0 0 5.37 0 12c0 5.3 3.438 9.8 8.205 11.385.6.113.82-.258.82-.577 0-.285-.01-1.04-.015-2.04-3.338.724-4.042-1.61-4.042-1.61-.546-1.385-1.335-1.755-1.335-1.755-1.087-.744.084-.729.084-.729 1.205.084 1.838 1.236 1.838 1.236 1.07 1.835 2.809 1.305 3.495.998.108-.776.417-1.305.76-1.605-2.665-.3-5.466-1.332-5.466-5.93 0-1.31.465-2.38 1.235-3.22-.135-.303-.54-1.523.105-3.176 0 0 1.005-.322 3.3 1.23.96-.267 1.98-.399 3-.405 1.02.006 2.04.138 3 .405 2.28-1.552 3.285-1.23 3.285-1.23.645 1.653.24 2.873.12 3.176.765.84 1.23 1.91 1.23 3.22 0 4.61-2.805 5.625-5.475 5.92.42.36.81 1.096.81 2.22 0 1.605-.015 2.896-.015 3.286 0 .315.21.69.825.57C20.565 21.795 24 17.295 24 12 24 5.37 18.63 0 12 0z"/></svg> Code</a>
      <a class="btn btn-outline" href="https://huggingface.co/tarzanagh/QAFD-RAG"><svg xmlns="http://www.w3.org/2000/svg" width="17" height="17" viewBox="0 0 95 88" fill="none"><path fill="#FFD21E" d="M47.21 76.5a34.75 34.75 0 1 0 0-69.5 34.75 34.75 0 0 0 0 69.5Z"/><path fill="#FF9D0B" d="M81.96 41.75a34.75 34.75 0 1 0-69.5 0 34.75 34.75 0 0 0 69.5 0Zm-73.5 0a38.75 38.75 0 1 1 77.5 0 38.75 38.75 0 0 1-77.5 0Z"/><path fill="#3A3B45" d="M58.5 32.3c1.28.44 1.78 3.06 3.07 2.38a5 5 0 1 0-6.76-2.07c.61 1.15 2.55-.72 3.7-.32ZM34.95 32.3c-1.28.44-1.79 3.06-3.07 2.38a5 5 0 1 1 6.76-2.07c-.61 1.15-2.56-.72-3.7-.32Z"/><path fill="#FF323D" d="M46.96 56.29c9.83 0 13-8.76 13-13.26 0-2.34-1.57-1.6-4.09-.36-2.33 1.15-5.46 2.74-8.9 2.74-7.19 0-13-6.88-13-2.38s3.16 13.26 13 13.26Z"/><path fill="#3A3B45" fill-rule="evenodd" d="M39.43 54a8.7 8.7 0 0 1 5.3-4.49c.4-.12.81.57 1.24 1.28.4.68.82 1.37 1.24 1.37.45 0 .9-.68 1.33-1.35.45-.7.89-1.38 1.32-1.25a8.61 8.61 0 0 1 5 4.17c3.73-2.94 5.1-7.74 5.1-10.7 0-2.34-1.57-1.6-4.09-.36l-.14.07c-2.31 1.15-5.39 2.67-8.77 2.67s-6.45-1.52-8.77-2.67c-2.6-1.29-4.23-2.1-4.23.29 0 3.05 1.46 8.06 5.47 10.97Z" clip-rule="evenodd"/><path fill="#FF9D0B" d="M70.71 37a3.25 3.25 0 1 0 0-6.5 3.25 3.25 0 0 0 0 6.5ZM24.21 37a3.25 3.25 0 1 0 0-6.5 3.25 3.25 0 0 0 0 6.5ZM17.52 48c-1.62 0-3.06.66-4.07 1.87a5.97 5.97 0 0 0-1.33 3.76 7.1 7.1 0 0 0-1.94-.3c-1.55 0-2.95.59-3.94 1.66a5.8 5.8 0 0 0-.8 7 5.3 5.3 0 0 0-1.79 2.82c-.24.9-.48 2.8.8 4.74a5.22 5.22 0 0 0-.37 5.02c1.02 2.32 3.57 4.14 8.52 6.1 3.07 1.22 5.89 2 5.91 2.01a44.33 44.33 0 0 0 10.93 1.6c5.86 0 10.05-1.8 12.46-5.34 3.88-5.69 3.33-10.9-1.7-15.92-2.77-2.78-4.62-6.87-5-7.77-.78-2.66-2.84-5.62-6.25-5.62a5.7 5.7 0 0 0-4.6 2.46c-1-1.26-1.98-2.25-2.86-2.82A7.4 7.4 0 0 0 17.52 48Zm0 4c.51 0 1.14.22 1.82.65 2.14 1.36 6.25 8.43 7.76 11.18.5.92 1.37 1.31 2.14 1.31 1.55 0 2.75-1.53.15-3.48-3.92-2.93-2.55-7.72-.68-8.01.08-.02.17-.02.24-.02 1.7 0 2.45 2.93 2.45 2.93s2.2 5.52 5.98 9.3c3.77 3.77 3.97 6.8 1.22 10.83-1.88 2.75-5.47 3.58-9.16 3.58-3.81 0-7.73-.9-9.92-1.46-.11-.03-13.45-3.8-11.76-7 .28-.54.75-.76 1.34-.76 2.38 0 6.7 3.54 8.57 3.54.41 0 .7-.17.83-.6.79-2.85-12.06-4.05-10.98-8.17.2-.73.71-1.02 1.44-1.02 3.14 0 10.2 5.53 11.68 5.53.11 0 .2-.03.24-.1.74-1.2.33-2.04-4.9-5.2-5.21-3.16-8.88-5.06-6.8-7.33.24-.26.58-.38 1-.38 3.17 0 10.66 6.82 10.66 6.82s2.02 2.1 3.25 2.1c.28 0 .52-.1.68-.38.86-1.46-8.06-8.22-8.56-11.01-.34-1.9.24-2.85 1.31-2.85Z"/><path fill="#FFD21E" d="M38.6 76.69c2.75-4.04 2.55-7.07-1.22-10.84-3.78-3.77-5.98-9.3-5.98-9.3s-.82-3.2-2.69-2.9c-1.87.3-3.24 5.08.68 8.01 3.91 2.93-.78 4.92-2.29 2.17-1.5-2.75-5.62-9.82-7.76-11.18-2.13-1.35-3.63-.6-3.13 2.2.5 2.79 9.43 9.55 8.56 11-.87 1.47-3.93-1.71-3.93-1.71s-9.57-8.71-11.66-6.44c-2.08 2.27 1.59 4.17 6.8 7.33 5.23 3.16 5.64 4 4.9 5.2-.75 1.2-12.28-8.53-13.36-4.4-1.08 4.11 11.77 5.3 10.98 8.15-.8 2.85-9.06-5.38-10.74-2.18-1.7 3.21 11.65 6.98 11.76 7.01 4.3 1.12 15.25 3.49 19.08-2.12Z"/><path fill="#FF9D0B" d="M77.4 48c1.62 0 3.07.66 4.07 1.87a5.97 5.97 0 0 1 1.33 3.76 7.1 7.1 0 0 1 1.95-.3c1.55 0 2.95.59 3.94 1.66a5.8 5.8 0 0 1 .8 7 5.3 5.3 0 0 1 1.78 2.82c.24.9.48 2.8-.8 4.74a5.22 5.22 0 0 1 .37 5.02c-1.02 2.32-3.57 4.14-8.51 6.1-3.08 1.22-5.9 2-5.92 2.01a44.33 44.33 0 0 1-10.93 1.6c-5.86 0-10.05-1.8-12.46-5.34-3.88-5.69-3.33-10.9 1.7-15.92 2.78-2.78 4.63-6.87 5.01-7.77.78-2.66 2.83-5.62 6.24-5.62a5.7 5.7 0 0 1 4.6 2.46c1-1.26 1.98-2.25 2.87-2.82A7.4 7.4 0 0 1 77.4 48Zm0 4c-.51 0-1.13.22-1.82.65-2.13 1.36-6.25 8.43-7.76 11.18a2.43 2.43 0 0 1-2.14 1.31c-1.54 0-2.75-1.53-.14-3.48 3.91-2.93 2.54-7.72.67-8.01a1.54 1.54 0 0 0-.24-.02c-1.7 0-2.45 2.93-2.45 2.93s-2.2 5.52-5.97 9.3c-3.78 3.77-3.98 6.8-1.22 10.83 1.87 2.75 5.47 3.58 9.15 3.58 3.82 0 7.73-.9 9.93-1.46.1-.03 13.45-3.8 11.76-7-.29-.54-.75-.76-1.34-.76-2.38 0-6.71 3.54-8.57 3.54-.42 0-.71-.17-.83-.6-.8-2.85 12.05-4.05 10.97-8.17-.19-.73-.7-1.02-1.44-1.02-3.14 0-10.2 5.53-11.68 5.53-.1 0-.19-.03-.23-.1-.74-1.2-.34-2.04 4.88-5.2 5.23-3.16 8.9-5.06 6.8-7.33-.23-.26-.57-.38-.98-.38-3.18 0-10.67 6.82-10.67 6.82s-2.02 2.1-3.24 2.1a.74.74 0 0 1-.68-.38c-.87-1.46 8.05-8.22 8.55-11.01.34-1.9-.24-2.85-1.31-2.85Z"/><path fill="#FFD21E" d="M56.33 76.69c-2.75-4.04-2.56-7.07 1.22-10.84 3.77-3.77 5.97-9.3 5.97-9.3s.82-3.2 2.7-2.9c1.86.3 3.23 5.08-.68 8.01-3.92 2.93.78 4.92 2.28 2.17 1.51-2.75 5.63-9.82 7.76-11.18 2.13-1.35 3.64-.6 3.13 2.2-.5 2.79-9.42 9.55-8.55 11 .86 1.47 3.92-1.71 3.92-1.71s9.58-8.71 11.66-6.44c2.08 2.27-1.58 4.17-6.8 7.33-5.23 3.16-5.63 4-4.9 5.2.75 1.2 12.28-8.53 13.36-4.4 1.08 4.11-11.76 5.3-10.97 8.15.8 2.85 9.05-5.38 10.74-2.18 1.69 3.21-11.65 6.98-11.76 7.01-4.31 1.12-15.26 3.49-19.08-2.12Z"/></svg> Code + Knowledge Graphs</a>
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</header>

<!-- ============ ABSTRACT ============ -->
<section>
  <div class="container">
    <h2 style="font-size:1.55rem;font-weight:700;color:var(--slate-800);margin-bottom:16px;">Query-Aware Flow Diffusion for Graph-Based<br/>Retrieval-Augmented Generation</h2>
    <p class="about-text" style="text-align:justify;">Graph-based RAG systems leverage interconnected knowledge structures to capture complex relationships, enabling multi-hop reasoning. Yet most existing methods suffer from (i) heuristic designs lacking theoretical guarantees and (ii) static exploration strategies that ignore the query&rsquo;s holistic meaning. We propose <strong style="color:var(--blue-600);">QAFD-RAG</strong>, a training-free framework that dynamically adapts graph traversal to each query&rsquo;s semantics. The central innovation is <em>query-aware traversal</em>: edges are dynamically weighted by how well their endpoints align with the query embedding, guiding flow along semantically relevant paths while suppressing irrelevant regions. This enables the <strong>first statistical guarantees</strong> for query-aware graph retrieval, with <strong>exponential convergence</strong> and complexity scaling with the retrieved subgraph rather than the full graph.</p>
  </div>
</section>

<!-- ============ KEY CONTRIBUTIONS ============ -->
<section class="alt">
  <div class="container">
    <h2>Key Contributions</h2>
    <div class="duo-grid" style="grid-template-columns:1fr 1fr 1fr;gap:16px;">
      <div class="card"><h3>Query-Aware Framework</h3><p>First principled flow diffusion method for graph-based RAG that incorporates query semantics via alignment-based edge weighting. Adapts flow probabilities <strong>online</strong>, guiding traversal toward semantically relevant regions.</p></div>
      <div class="card"><h3>Provable Guarantees</h3><p><strong>Exponential convergence</strong> to a query-dependent stationary distribution. <strong>Recovery guarantees</strong> ensuring relevant subgraphs are retrieved with high probability under mild signal-to-noise conditions.</p></div>
      <div class="card"><h3>State-of-the-Art Results</h3><p>Leads in <strong>96%</strong> of UltraDomain comparisons. Best F1/EM on HotpotQA (<strong>73.4/58.1</strong>) and MuSiQue (<strong>48.0/33.5</strong>). Outperforms GraphRAG, LightRAG, and RAPTOR across all benchmarks.</p></div>
    </div>
  </div>
</section>

<!-- ============ APPROACH COMPARISON ============ -->
<section>
  <div class="container">
    <h2>Approach Comparison</h2>
    <p class="section-sub">Query: <em>&ldquo;Introduce Steve Jobs&rsquo;s products in Apple.&rdquo;</em></p>
    <div class="figure-row">
      <div class="figure-card"><img src="figs/GraphRAG.png" alt="GraphRAG"/><div class="caption">GraphRAG<br/><small>Community Detection</small></div></div>
      <div class="figure-card"><img src="figs/LightRAG.png" alt="LightRAG"/><div class="caption">LightRAG<br/><small>One-Hop Entity-Centric</small></div></div>
      <div class="figure-card"><img src="figs/QAFD-RAG.png" alt="QAFD-RAG"/><div class="caption">QAFD-RAG (Ours)<br/><small>Query-Aware Flow Diffusion</small></div></div>
    </div>
    <p style="margin-top:24px;font-size:0.92rem;color:var(--slate-500);line-height:1.75;max-width:860px;margin-left:auto;margin-right:auto;"><strong style="color:var(--slate-700);">GraphRAG</strong> retrieves entire communities, mixing relevant and irrelevant nodes. <strong style="color:var(--slate-700);">LightRAG</strong> extracts 1-hop neighborhoods without semantic alignment. <strong style="color:var(--slate-700);">QAFD-RAG</strong> reweights edges by query meaning, suppressing irrelevant clusters (Amazon River, Apple fruit) and reinforcing reasoning paths (Apple &rarr; Mac &rarr; macOS). Edge thickness reflects weight; node color indicates importance.</p>
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</section>

<!-- ============ HOW IT WORKS ============ -->
<section class="alt">
  <div class="container">
    <h2>How It Works</h2>
    <p class="section-sub">A two-stage pipeline from raw documents to grounded answers</p>
    <div class="duo-grid">
      <div class="card"><h3>Stage 1 &mdash; Knowledge Graph Construction</h3><ol><li><strong>Document Chunking</strong> &mdash; Split into context-preserving chunks.</li><li><strong>Entity &amp; Relationship Extraction</strong> &mdash; LLM builds a structured KG with entities as nodes and relationships as edges.</li><li><strong>Embedding</strong> &mdash; All nodes embedded into vector space for similarity matching.</li></ol></div>
      <div class="card"><h3>Stage 2 &mdash; Query-Aware Retrieval</h3><ol><li><strong>Seed Selection</strong> &mdash; Query matched to KG entities via embedding similarity; LLM reranker filters top seeds.</li><li><strong>Flow Diffusion</strong> &mdash; Mass injected at seeds and propagated via push-relabel with <em>query-aware edge weights</em>.</li><li><strong>Response Generation</strong> &mdash; Top-ranked subgraph assembled into context for LLM answer generation.</li></ol></div>
    </div>
  </div>
</section>

<!-- ============ BENCHMARKS ============ -->
<section>
  <div class="container">
    <h2>Benchmarks</h2>
    <p class="section-sub">Evaluated on UltraDomain QA (11 domains), multi-hop QA, text-to-SQL, and summarization. Full results in the <a href="https://openreview.net/pdf?id=n28wnc2QTc" style="color:var(--blue-600);">paper</a>.</p>
    <div class="bench-grid">
      <div class="bench-item"><div class="task">UltraDomain QA</div><div class="dataset">11 domains &middot; 5 quality metrics</div><div class="metrics">Leads in <strong>96%</strong> of comparisons (48/50)</div></div>
      <div class="bench-item"><div class="task">Multi-hop QA</div><div class="dataset">MuSiQue &middot; HotpotQA &middot; 2Wiki</div><div class="metrics">Best F1 on HotpotQA (<strong>73.4</strong>) &amp; MuSiQue (<strong>48.0</strong>)</div></div>
      <div class="bench-item"><div class="task">Text-to-SQL</div><div class="dataset">Spider2-lite (SQLite &middot; Snowflake)</div><div class="metrics"><strong>26.7%</strong> SQLite &middot; <strong>23.7%</strong> Snowflake</div></div>
      <div class="bench-item"><div class="task">Summarization</div><div class="dataset">SQuALITY</div><div class="metrics">BLEU &middot; ROUGE &middot; METEOR</div></div>
    </div>
  </div>
</section>

<!-- ============ QUICK START ============ -->
<section class="alt">
  <div class="container">
    <h2>Quick Start</h2>
    <p class="section-sub">Get running in minutes with pre-built knowledge graphs</p>
<pre><code><span class="comment"># Option 1: Clone from HuggingFace (code + pre-built KGs)</span>
git clone https://huggingface.co/tarzanagh/QAFD-RAG
<span class="keyword">cd</span> QAFD-RAG

<span class="comment"># Option 2: Clone from GitHub (code only) + download KGs</span>
git clone https://github.com/Tarzanagh/QAFD-RAG.git
<span class="keyword">cd</span> QAFD-RAG
huggingface-cli download tarzanagh/QAFD-RAG --include <span class="string">"kg/multihop/*"</span> --local-dir .

<span class="comment"># Install and run</span>
pip install -r requirements.txt
export OPENAI_API_KEY=<span class="string">"sk-..."</span>
python benchmarks/run.py --task multihop --dataset musique --questions 10</code></pre>
  </div>
</section>

<!-- ============ CITATION ============ -->
<section>
  <div class="container">
    <h2>Citation</h2>
<pre><code>@inproceedings{zhou2026qafd,
  title={Query-Aware Flow Diffusion for Graph-Based RAG with Retrieval Guarantees},
  author={Zhou, Zhuoping and Ataee Tarzanagh, Davoud and Didari, Sima and Hu, Wenjun
          and Gutow, Baruch and Verkholyak, Oxana and Faraki, Masoud and Hao, Heng
          and Moon, Hankyu and Min, Seungjai},
  booktitle={International Conference on Learning Representations (ICLR)},
  year={2026}
}</code></pre>
  </div>
</section>

<footer>
  <p>QAFD-RAG <span class="sep">·</span><a href="https://openreview.net/pdf?id=n28wnc2QTc">Paper</a> <span class="sep">·</span><a href="https://github.com/Tarzanagh/QAFD-RAG">GitHub</a> <span class="sep">·</span><a href="https://huggingface.co/tarzanagh/QAFD-RAG">HuggingFace</a></p>
  <p style="margin-top:8px;opacity:0.6;">Contact: tarzanagh [at] gmail [dot] com</p>
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