diff --git a/fuzz-testing/src/main/scala/org/apache/comet/fuzz/Meta.scala b/fuzz-testing/src/main/scala/org/apache/comet/fuzz/Meta.scala
index 74d13f85ee..7ffec3b5af 100644
--- a/fuzz-testing/src/main/scala/org/apache/comet/fuzz/Meta.scala
+++ b/fuzz-testing/src/main/scala/org/apache/comet/fuzz/Meta.scala
@@ -43,6 +43,7 @@ case class SparkArrayType(elementType: SparkType) extends SparkType
 case class SparkMapType(keyType: SparkType, valueType: SparkType) extends SparkType
 case class SparkStructType(fields: Seq[SparkType]) extends SparkType
 case object SparkAnyType extends SparkType
+case class SparkTypeWithValues(sparkType: SparkType, validValues: Seq[String]) extends SparkType
 
 case class FunctionSignature(inputTypes: Seq[SparkType])
 
@@ -302,7 +303,12 @@ object Meta {
       createFunctionWithInputTypes("hour", Seq(SparkDateOrTimestampType)),
       createFunctionWithInputTypes("minute", Seq(SparkDateOrTimestampType)),
       createFunctionWithInputTypes("second", Seq(SparkDateOrTimestampType)),
-      createFunctionWithInputTypes("trunc", Seq(SparkDateOrTimestampType, SparkStringType)),
+      createFunctionWithInputTypes(
+        "date_trunc",
+        Seq(SparkDateOrTimestampType, SparkTypeWithValues(SparkStringType, Seq("year", "week")))),
+      createFunctionWithInputTypes(
+        "trunc",
+        Seq(SparkDateOrTimestampType, SparkTypeWithValues(SparkStringType, Seq("year", "week")))),
       createFunctionWithInputTypes("year", Seq(SparkDateOrTimestampType)),
       createFunctionWithInputTypes("month", Seq(SparkDateOrTimestampType)),
       createFunctionWithInputTypes("day", Seq(SparkDateOrTimestampType)),
diff --git a/fuzz-testing/src/main/scala/org/apache/comet/fuzz/QueryGen.scala b/fuzz-testing/src/main/scala/org/apache/comet/fuzz/QueryGen.scala
index d9e3c147d2..4b53b33897 100644
--- a/fuzz-testing/src/main/scala/org/apache/comet/fuzz/QueryGen.scala
+++ b/fuzz-testing/src/main/scala/org/apache/comet/fuzz/QueryGen.scala
@@ -103,7 +103,7 @@ object QueryGen {
     val func = Utils.randomChoice(Meta.scalarFunc, r)
     try {
       val signature = Utils.randomChoice(func.signatures, r)
-      val args = signature.inputTypes.map(x => pickRandomColumn(r, table, x))
+      val args = signature.inputTypes.map(x => pickRandomColumnOrLiteral(r, table, x))
 
       // Example SELECT c0, log(c0) as x FROM test0
       s"SELECT ${args.mkString(", ")}, ${func.name}(${args.mkString(", ")}) AS x " +
@@ -117,6 +117,40 @@ object QueryGen {
     }
   }
 
+  private def pickRandomColumnOrLiteral(
+      r: Random,
+      df: DataFrame,
+      targetType: SparkType): String = {
+    if (r.nextBoolean) {
+      targetType match {
+        case SparkIntegralType =>
+          r.nextInt(10).toString
+        case SparkStringType =>
+          formatLiteral(r.nextString(4), SparkStringType)
+        case SparkTimestampType =>
+          "now()"
+        case SparkTypeWithValues(sparkType, values) =>
+          // choose between known valid input and random input
+          if (r.nextBoolean()) {
+            formatLiteral(Utils.randomChoice(values, r), sparkType)
+          } else {
+            pickRandomColumnOrLiteral(r, df, sparkType)
+          }
+        case _ =>
+          pickRandomColumn(r, df, targetType)
+      }
+    } else {
+      pickRandomColumn(r, df, targetType)
+    }
+  }
+
+  private def formatLiteral(validValue: Any, sparkType: SparkType): String = {
+    sparkType match {
+      case SparkStringType => s""""$validValue""""
+      case _ => validValue.toString
+    }
+  }
+
   private def pickRandomColumn(r: Random, df: DataFrame, targetType: SparkType): String = {
     targetType match {
       case SparkAnyType =>