{
  "article_slug": "diffusion-guidance-bias",
  "figures": [
    {
      "id": "guided-gaussian",
      "title": "Guidance changes mean and spread",
      "kind": "analytical_curve",
      "x_label": "Guidance g (g=1 conditional)",
      "y_label": "Mean / variance",
      "x": {
        "name": "Guidance g (g=1 conditional)",
        "values": [
          0,
          0.25,
          0.5,
          0.75,
          1,
          1.25,
          1.5,
          2,
          3,
          4
        ]
      },
      "series": [
        {
          "name": "Mean",
          "values": [
            0.0,
            0.5714285714285714,
            0.8,
            0.9230769230769231,
            1.0,
            1.0526315789473684,
            1.0909090909090908,
            1.1428571428571428,
            1.2,
            1.2307692307692308
          ]
        },
        {
          "name": "Variance",
          "values": [
            1.0,
            0.5714285714285714,
            0.4,
            0.3076923076923077,
            0.25,
            0.21052631578947367,
            0.18181818181818182,
            0.14285714285714285,
            0.1,
            0.07692307692307693
          ]
        }
      ],
      "caption": "Exact fixed-noise p_u=N(0,1), p_c=N(1,0.25), score s_u+g(s_c-s_u). Not an endpoint law for a complete diffusion sampler."
    },
    {
      "id": "normalizability-boundary",
      "title": "A wider conditional can lose normalizability",
      "kind": "analytical_curve",
      "x_label": "Guidance g",
      "y_label": "Precision tau",
      "x": {
        "name": "Guidance g",
        "values": [
          0,
          0.25,
          0.5,
          0.75,
          1,
          1.25,
          1.5,
          2,
          3,
          4
        ]
      },
      "series": [
        {
          "name": "Conditional variance4",
          "values": [
            1.0,
            0.8125,
            0.625,
            0.4375,
            0.25,
            0.0625,
            -0.125,
            -0.5,
            -1.25,
            -2.0
          ]
        },
        {
          "name": "Zero precision boundary",
          "values": [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0
          ]
        }
      ],
      "caption": "Exact fixed-noise construction with p_c=N(1,4). The power product is normalizable only where tau>0; g>=4/3 is invalid. No finite variance is assigned to invalid points."
    }
  ]
}