diff --git a/app/androidApp/src/main/kotlin/com/example/aiapp/SessionImage.kt b/app/androidApp/src/main/kotlin/com/example/aiapp/SessionImage.kt
index e440b1c..0056e9b 100644
--- a/app/androidApp/src/main/kotlin/com/example/aiapp/SessionImage.kt
+++ b/app/androidApp/src/main/kotlin/com/example/aiapp/SessionImage.kt
@@ -23,6 +23,7 @@ import androidx.compose.runtime.setValue
 import androidx.compose.ui.Alignment
 import androidx.compose.ui.Modifier
 import androidx.compose.ui.draw.clip
+import androidx.compose.ui.geometry.Offset
 import androidx.compose.ui.graphics.Color
 import androidx.compose.ui.graphics.FilterQuality
 import androidx.compose.ui.graphics.ImageBitmap
@@ -242,17 +243,28 @@ private fun ZoomableImage(image: ImageBitmap) {
         modifier =
             Modifier.fillMaxSize()
                 .pointerInput(Unit) {
-                    detectTransformGestures { _, pan, zoom, _ ->
+                    detectTransformGestures { centroid, pan, zoom, _ ->
                         // Floor of 1 so the image cannot be pinched smaller than fitted, which is
                         // already the whole of it; a ceiling so it cannot be lost off-screen.
-                        scale = (scale * zoom).coerceIn(1f, 8f)
-                        if (scale > 1f) {
-                            offsetX += pan.x
-                            offsetY += pan.y
+                        val oldScale = scale
+                        val newScale = (oldScale * zoom).coerceIn(1f, 8f)
+                        if (newScale > 1f) {
+                            val offset =
+                                zoomOffset(
+                                    Offset(offsetX, offsetY),
+                                    centroid,
+                                    pan,
+                                    oldScale,
+                                    newScale,
+                                    Offset(size.width / 2f, size.height / 2f),
+                                )
+                            offsetX = offset.x
+                            offsetY = offset.y
                         } else {
                             offsetX = 0f
                             offsetY = 0f
                         }
+                        scale = newScale
                     }
                 }
                 .graphicsLayer {
@@ -263,3 +275,16 @@ private fun ZoomableImage(image: ImageBitmap) {
                 },
     )
 }
+
+/** Keeps the image point beneath [centroid] beneath the fingers as its scale changes. */
+internal fun zoomOffset(
+    offset: Offset,
+    centroid: Offset,
+    pan: Offset,
+    oldScale: Float,
+    newScale: Float,
+    viewportCenter: Offset,
+): Offset {
+    val scaleChange = newScale / oldScale
+    return offset * scaleChange + (centroid - viewportCenter) * (1f - scaleChange) + pan
+}
diff --git a/app/androidApp/src/test/kotlin/com/example/aiapp/SessionImageTest.kt b/app/androidApp/src/test/kotlin/com/example/aiapp/SessionImageTest.kt
new file mode 100644
index 0000000..a7fff9c
--- /dev/null
+++ b/app/androidApp/src/test/kotlin/com/example/aiapp/SessionImageTest.kt
@@ -0,0 +1,37 @@
+package com.example.aiapp
+
+import androidx.compose.ui.geometry.Offset
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+class SessionImageTest {
+    @Test
+    fun `zoom keeps the region panned to in the center`() {
+        assertEquals(
+            Offset(240f, -160f),
+            zoomOffset(
+                offset = Offset(120f, -80f),
+                centroid = Offset(500f, 1000f),
+                pan = Offset.Zero,
+                oldScale = 2f,
+                newScale = 4f,
+                viewportCenter = Offset(500f, 1000f),
+            ),
+        )
+    }
+
+    @Test
+    fun `zoom keeps an off-center pinch beneath moving fingers`() {
+        assertEquals(
+            Offset(460f, 420f),
+            zoomOffset(
+                offset = Offset(100f, -100f),
+                centroid = Offset(250f, 400f),
+                pan = Offset(10f, 20f),
+                oldScale = 2f,
+                newScale = 4f,
+                viewportCenter = Offset(500f, 1000f),
+            ),
+        )
+    }
+}