diff --git a/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Continuous.res b/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Continuous.res
index 1467239e..06c54040 100644
--- a/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Continuous.res
+++ b/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Continuous.res
@@ -271,12 +271,22 @@ module T = Dist({
     XYShape.Analysis.getVarianceDangerously(t, mean, Analysis.getMeanOfSquares)
 
   let logScore = (base: t, reference: t) => {
-    E.R2.bind(
-      combinePointwise(PointSetDist_Scoring.LogScoring.multiply, reference),
-      combinePointwise(PointSetDist_Scoring.LogScoring.logScore, base, reference),
-    )
-    |> E.R.fmap(shapeMap(XYShape.T.filterYValues(Js.Float.isFinite)))
-    |> E.R.fmap(integralEndY)
+    let referenceIsZero = switch Distributions.Common.isZeroEverywhere(
+      PointSetTypes.Continuous(reference),
+    ) {
+    | Continuous(b) => b
+    | _ => false
+    }
+    if referenceIsZero {
+      Ok(0.0)
+    } else {
+      E.R2.bind(
+        combinePointwise(PointSetDist_Scoring.LogScoring.multiply, reference),
+        combinePointwise(PointSetDist_Scoring.LogScoring.logScore, base, reference),
+      )
+      |> E.R.fmap(shapeMap(XYShape.T.filterYValues(Js.Float.isFinite)))
+      |> E.R.fmap(integralEndY)
+    }
   }
 })
 
diff --git a/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Discrete.res b/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Discrete.res
index a6c04e6b..a74283dd 100644
--- a/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Discrete.res
+++ b/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Discrete.res
@@ -230,8 +230,19 @@ module T = Dist({
   }
 
   let logScore = (base: t, reference: t) => {
-    combinePointwise(~fn=PointSetDist_Scoring.LogScoring.logScore, base, reference) |> E.R2.bind(
-      integralEndYResult,
-    )
+    let referenceIsZero = switch Distributions.Common.isZeroEverywhere(
+      PointSetTypes.Discrete(reference),
+    ) {
+    | Discrete(b) => b
+    | _ => false
+    }
+    if referenceIsZero {
+      Ok(0.0)
+    } else {
+      E.R2.bind(
+        combinePointwise(~fn=PointSetDist_Scoring.LogScoring.multiply, reference),
+        combinePointwise(~fn=PointSetDist_Scoring.LogScoring.logScore, base, reference),
+      ) |> E.R2.bind(integralEndYResult)
+    }
   }
 })
diff --git a/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Distributions.res b/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Distributions.res
index 15da318d..0ad3b24a 100644
--- a/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Distributions.res
+++ b/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Distributions.res
@@ -96,4 +96,18 @@ module Common = {
       None
     | (Some(s1), Some(s2)) => combineFn(s1, s2)
     }
+
+  let isZeroEverywhere = (d: PointSetTypes.pointSetDist) => {
+    let isZero = (x: float): bool => x == 0.0
+    PointSetTypes.ShapeMonad.fmap(
+      d,
+      (
+        mixed =>
+          E.A.all(isZero, mixed.continuous.xyShape.ys) &&
+          E.A.all(isZero, mixed.discrete.xyShape.ys),
+        disc => E.A.all(isZero, disc.xyShape.ys),
+        cont => E.A.all(isZero, cont.xyShape.ys),
+      ),
+    )
+  }
 }
diff --git a/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Mixed.res b/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Mixed.res
index 3d36d421..0e528496 100644
--- a/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Mixed.res
+++ b/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Mixed.res
@@ -302,9 +302,20 @@ module T = Dist({
   }
 
   let logScore = (base: t, reference: t) => {
-    combinePointwise(PointSetDist_Scoring.LogScoring.logScore, base, reference) |> E.R.fmap(
-      integralEndY,
-    )
+    let referenceIsZero = switch Distributions.Common.isZeroEverywhere(
+      PointSetTypes.Mixed(reference),
+    ) {
+    | Mixed(b) => b
+    | _ => false
+    }
+    if referenceIsZero {
+      Ok(0.0)
+    } else {
+      E.R2.bind(
+        combinePointwise(PointSetDist_Scoring.LogScoring.multiply, reference),
+        combinePointwise(PointSetDist_Scoring.LogScoring.logScore, base, reference),
+      ) |> E.R.fmap(integralEndY)
+    }
   }
 })
 
diff --git a/packages/squiggle-lang/src/rescript/Utility/E.res b/packages/squiggle-lang/src/rescript/Utility/E.res
index 472c32f7..076fc89f 100644
--- a/packages/squiggle-lang/src/rescript/Utility/E.res
+++ b/packages/squiggle-lang/src/rescript/Utility/E.res
@@ -606,6 +606,9 @@ module A = {
   let filter = Js.Array.filter
   let joinWith = Js.Array.joinWith
 
+  let all = (p: 'a => bool, xs: array<'a>): bool => length(filter(p, xs)) == length(xs)
+  let any = (p: 'a => bool, xs: array<'a>): bool => length(filter(p, xs)) > 0
+
   module O = {
     let concatSomes = (optionals: array<option<'a>>): array<'a> =>
       optionals