diff --git a/analysis/low-level-api-fir/tests/org/jetbrains/kotlin/analysis/low/level/api/fir/diagnostic/compiler/based/DiagnosticCompilerTestFE10TestdataTestGenerated.java b/analysis/low-level-api-fir/tests/org/jetbrains/kotlin/analysis/low/level/api/fir/diagnostic/compiler/based/DiagnosticCompilerTestFE10TestdataTestGenerated.java
index a72669a5798..d6c2f2c8150 100644
--- a/analysis/low-level-api-fir/tests/org/jetbrains/kotlin/analysis/low/level/api/fir/diagnostic/compiler/based/DiagnosticCompilerTestFE10TestdataTestGenerated.java
+++ b/analysis/low-level-api-fir/tests/org/jetbrains/kotlin/analysis/low/level/api/fir/diagnostic/compiler/based/DiagnosticCompilerTestFE10TestdataTestGenerated.java
@@ -195,6 +195,12 @@ public class DiagnosticCompilerTestFE10TestdataTestGenerated extends AbstractDia
             runTest("compiler/testData/diagnostics/tests/comparisonOfGenericInterfaceWithGenericClass.kt");
         }
 
+        @Test
+        @TestMetadata("compilerCrashParameterType.kt")
+        public void testCompilerCrashParameterType() throws Exception {
+            runTest("compiler/testData/diagnostics/tests/compilerCrashParameterType.kt");
+        }
+
         @Test
         @TestMetadata("Constants.kt")
         public void testConstants() throws Exception {
diff --git a/analysis/low-level-api-fir/tests/org/jetbrains/kotlin/analysis/low/level/api/fir/diagnostic/compiler/based/LLFirPreresolvedReversedDiagnosticCompilerFE10TestDataTestGenerated.java b/analysis/low-level-api-fir/tests/org/jetbrains/kotlin/analysis/low/level/api/fir/diagnostic/compiler/based/LLFirPreresolvedReversedDiagnosticCompilerFE10TestDataTestGenerated.java
index bc30a728984..4752162bc2e 100644
--- a/analysis/low-level-api-fir/tests/org/jetbrains/kotlin/analysis/low/level/api/fir/diagnostic/compiler/based/LLFirPreresolvedReversedDiagnosticCompilerFE10TestDataTestGenerated.java
+++ b/analysis/low-level-api-fir/tests/org/jetbrains/kotlin/analysis/low/level/api/fir/diagnostic/compiler/based/LLFirPreresolvedReversedDiagnosticCompilerFE10TestDataTestGenerated.java
@@ -195,6 +195,12 @@ public class LLFirPreresolvedReversedDiagnosticCompilerFE10TestDataTestGenerated
             runTest("compiler/testData/diagnostics/tests/comparisonOfGenericInterfaceWithGenericClass.kt");
         }
 
+        @Test
+        @TestMetadata("compilerCrashParameterType.kt")
+        public void testCompilerCrashParameterType() throws Exception {
+            runTest("compiler/testData/diagnostics/tests/compilerCrashParameterType.kt");
+        }
+
         @Test
         @TestMetadata("Constants.kt")
         public void testConstants() throws Exception {
diff --git a/compiler/fir/analysis-tests/testData/resolve/cast.kt b/compiler/fir/analysis-tests/testData/resolve/cast.kt
index 25782fdfc86..d322b0af741 100644
--- a/compiler/fir/analysis-tests/testData/resolve/cast.kt
+++ b/compiler/fir/analysis-tests/testData/resolve/cast.kt
@@ -4,4 +4,4 @@ val y = 2 as Any
 val f = fun() = 3 as Any
 val g = {}
 val h: (String) -> Boolean = { _ -> false }
-val hError = { _ -> true }
+val hError = { <!VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>_<!> -> true }
diff --git a/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/test/runners/FirLightTreeOldFrontendDiagnosticsTestGenerated.java b/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/test/runners/FirLightTreeOldFrontendDiagnosticsTestGenerated.java
index 71120ce37ec..822e8351bfe 100644
--- a/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/test/runners/FirLightTreeOldFrontendDiagnosticsTestGenerated.java
+++ b/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/test/runners/FirLightTreeOldFrontendDiagnosticsTestGenerated.java
@@ -195,6 +195,12 @@ public class FirLightTreeOldFrontendDiagnosticsTestGenerated extends AbstractFir
             runTest("compiler/testData/diagnostics/tests/comparisonOfGenericInterfaceWithGenericClass.kt");
         }
 
+        @Test
+        @TestMetadata("compilerCrashParameterType.kt")
+        public void testCompilerCrashParameterType() throws Exception {
+            runTest("compiler/testData/diagnostics/tests/compilerCrashParameterType.kt");
+        }
+
         @Test
         @TestMetadata("Constants.kt")
         public void testConstants() throws Exception {
diff --git a/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/test/runners/FirPsiOldFrontendDiagnosticsTestGenerated.java b/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/test/runners/FirPsiOldFrontendDiagnosticsTestGenerated.java
index c6d5c755ccc..ca2f0a5b632 100644
--- a/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/test/runners/FirPsiOldFrontendDiagnosticsTestGenerated.java
+++ b/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/test/runners/FirPsiOldFrontendDiagnosticsTestGenerated.java
@@ -195,6 +195,12 @@ public class FirPsiOldFrontendDiagnosticsTestGenerated extends AbstractFirPsiDia
             runTest("compiler/testData/diagnostics/tests/comparisonOfGenericInterfaceWithGenericClass.kt");
         }
 
+        @Test
+        @TestMetadata("compilerCrashParameterType.kt")
+        public void testCompilerCrashParameterType() throws Exception {
+            runTest("compiler/testData/diagnostics/tests/compilerCrashParameterType.kt");
+        }
+
         @Test
         @TestMetadata("Constants.kt")
         public void testConstants() throws Exception {
diff --git a/compiler/fir/checkers/src/org/jetbrains/kotlin/fir/analysis/diagnostics/coneDiagnosticToFirDiagnostic.kt b/compiler/fir/checkers/src/org/jetbrains/kotlin/fir/analysis/diagnostics/coneDiagnosticToFirDiagnostic.kt
index bb077fef84a..33c259aeeb7 100644
--- a/compiler/fir/checkers/src/org/jetbrains/kotlin/fir/analysis/diagnostics/coneDiagnosticToFirDiagnostic.kt
+++ b/compiler/fir/checkers/src/org/jetbrains/kotlin/fir/analysis/diagnostics/coneDiagnosticToFirDiagnostic.kt
@@ -118,7 +118,7 @@ private fun ConeDiagnostic.toKtDiagnostic(
     is ConeSyntaxDiagnostic -> FirSyntaxErrors.SYNTAX.createOn(callOrAssignmentSource ?: source, reason)
 
     is ConeSimpleDiagnostic -> when {
-        source?.kind is KtFakeSourceElementKind && source.kind != KtFakeSourceElementKind.ReferenceInAtomicQualifiedAccess -> null
+        (source?.kind as? KtFakeSourceElementKind)?.canBeIgnored == true -> null
         else -> this.getFactory(source).createOn(callOrAssignmentSource ?: source)
     }
 
@@ -155,6 +155,10 @@ private fun ConeDiagnostic.toKtDiagnostic(
     else -> throw IllegalArgumentException("Unsupported diagnostic type: ${this.javaClass}")
 }
 
+private val KtFakeSourceElementKind.canBeIgnored: Boolean
+    get() = this != KtFakeSourceElementKind.ReferenceInAtomicQualifiedAccess
+            && this != KtFakeSourceElementKind.ImplicitReturnTypeOfLambdaValueParameter
+
 fun FirBasedSymbol<*>.toInvisibleReferenceDiagnostic(source: KtSourceElement?): KtDiagnostic? = when (val symbol = this) {
     is FirCallableSymbol<*> -> FirErrors.INVISIBLE_REFERENCE.createOn(source, symbol, symbol.visibility, symbol.callableId.classId)
     is FirClassLikeSymbol<*> -> FirErrors.INVISIBLE_REFERENCE.createOn(source, symbol, symbol.visibility, symbol.classId.outerClassId)
diff --git a/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/transformers/body/resolve/FirDeclarationsResolveTransformer.kt b/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/transformers/body/resolve/FirDeclarationsResolveTransformer.kt
index 9a0315107c9..18d92fa46a7 100644
--- a/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/transformers/body/resolve/FirDeclarationsResolveTransformer.kt
+++ b/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/transformers/body/resolve/FirDeclarationsResolveTransformer.kt
@@ -1077,7 +1077,10 @@ open class FirDeclarationsResolveTransformer(
                                     "No type for parameter",
                                     DiagnosticKind.ValueParameterWithNoTypeAnnotation
                                 )
-                            )
+                            ),
+                            fallbackSource = valueParameter.source?.fakeElement(
+                                KtFakeSourceElementKind.ImplicitReturnTypeOfLambdaValueParameter,
+                            ),
                         )
                     )
                 }
diff --git a/compiler/testData/diagnostics/tests/FunctionParameterWithoutType.fir.kt b/compiler/testData/diagnostics/tests/FunctionParameterWithoutType.fir.kt
index 39353186ddc..2900060d260 100644
--- a/compiler/testData/diagnostics/tests/FunctionParameterWithoutType.fir.kt
+++ b/compiler/testData/diagnostics/tests/FunctionParameterWithoutType.fir.kt
@@ -5,7 +5,7 @@ fun test(<!VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>a<!>, <!VALUE_PARAMETER_WITH
 
 class A(a<!SYNTAX!><!>)
 
-val bar = fun(a){}
+val bar = fun(<!VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>a<!>){}
 
-val la = { a -> }
+val la = { <!VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>a<!> -> }
 val las = { a: Int -> }
diff --git a/compiler/testData/diagnostics/tests/compilerCrashParameterType.fir.kt b/compiler/testData/diagnostics/tests/compilerCrashParameterType.fir.kt
new file mode 100644
index 00000000000..40a62bf8336
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/compilerCrashParameterType.fir.kt
@@ -0,0 +1,8 @@
+// ISSUE: KT-58906
+
+fun someFun(i: Int) = 42
+fun someSad(i: () -> String) = 42
+
+fun main(args: Array<String>) {
+    { <!VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>x<!> -> someFun(x) } //here should be CANNOT_INFER_PARAMETER_TYPE
+}
diff --git a/compiler/testData/diagnostics/tests/compilerCrashParameterType.kt b/compiler/testData/diagnostics/tests/compilerCrashParameterType.kt
new file mode 100644
index 00000000000..ac0d463e0d1
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/compilerCrashParameterType.kt
@@ -0,0 +1,8 @@
+// ISSUE: KT-58906
+
+fun someFun(i: Int) = 42
+fun someSad(i: () -> String) = 42
+
+fun main(args: Array<String>) {
+    { <!CANNOT_INFER_PARAMETER_TYPE!>x<!> -> someFun(<!DEBUG_INFO_ELEMENT_WITH_ERROR_TYPE!>x<!>) } //here should be CANNOT_INFER_PARAMETER_TYPE
+}
diff --git a/compiler/testData/diagnostics/tests/functionAsExpression/MissingParameterTypes.fir.kt b/compiler/testData/diagnostics/tests/functionAsExpression/MissingParameterTypes.fir.kt
index a53c1ba8f57..d3f9250447c 100644
--- a/compiler/testData/diagnostics/tests/functionAsExpression/MissingParameterTypes.fir.kt
+++ b/compiler/testData/diagnostics/tests/functionAsExpression/MissingParameterTypes.fir.kt
@@ -1,7 +1,7 @@
 // !CHECK_TYPE
 // !DIAGNOSTICS: -UNUSED_PARAMETER -UNUSED_ANONYMOUS_PARAMETER -UNUSED_VARIABLE
 
-val a = fun (x) = x
+val a = fun (<!VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>x<!>) = x
 
 val b: (Int) -> Int = fun (x) = x + 3
 
diff --git a/compiler/testData/diagnostics/tests/functionLiterals/DeprecatedSyntax.fir.kt b/compiler/testData/diagnostics/tests/functionLiterals/DeprecatedSyntax.fir.kt
index cc8a8b93bde..456a84941cd 100644
--- a/compiler/testData/diagnostics/tests/functionLiterals/DeprecatedSyntax.fir.kt
+++ b/compiler/testData/diagnostics/tests/functionLiterals/DeprecatedSyntax.fir.kt
@@ -9,8 +9,8 @@ val returnTypeWithParameter = { <!COMPONENT_FUNCTION_MISSING!>(b: Int): Int<!> -
 
 val receiverWithFunctionType = { ((Int)<!SYNTAX!><!> <!SYNTAX!>-> Int).() -><!> }
 
-val parenthesizedParameters = { <!COMPONENT_FUNCTION_MISSING!>(a: Int)<!> -> }
-val parenthesizedParameters2 = { <!COMPONENT_FUNCTION_MISSING!>(b)<!> -> }
+val parenthesizedParameters = { <!COMPONENT_FUNCTION_MISSING, VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>(a: Int)<!> -> }
+val parenthesizedParameters2 = { <!COMPONENT_FUNCTION_MISSING, VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>(b)<!> -> }
 
 val none = { -> }
 
@@ -18,7 +18,7 @@ val none = { -> }
 val parameterWithFunctionType = { a: ((Int) -> Int) -> <!SYNTAX!><!>} // todo fix parser
 
 val newSyntax = { a: Int -> }
-val newSyntax1 = { a, b -> }
+val newSyntax1 = { <!VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>a<!>, <!VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>b<!> -> }
 val newSyntax2 = { a: Int, b: Int -> }
-val newSyntax3 = { a, b: Int -> }
-val newSyntax4 = { a: Int, b -> }
+val newSyntax3 = { <!VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>a<!>, b: Int -> }
+val newSyntax4 = { a: Int, <!VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>b<!> -> }
diff --git a/compiler/testData/diagnostics/tests/functionLiterals/destructuringInLambdas/noExpectedType.fir.kt b/compiler/testData/diagnostics/tests/functionLiterals/destructuringInLambdas/noExpectedType.fir.kt
index 4a176c8f6b1..fcc7a7a57cd 100644
--- a/compiler/testData/diagnostics/tests/functionLiterals/destructuringInLambdas/noExpectedType.fir.kt
+++ b/compiler/testData/diagnostics/tests/functionLiterals/destructuringInLambdas/noExpectedType.fir.kt
@@ -24,7 +24,7 @@ fun bar() {
 
     y2 checkType { _<(A) -> Unit>() }
 
-    val z = { <!COMPONENT_FUNCTION_MISSING, COMPONENT_FUNCTION_MISSING!>(a: Int, b: String)<!> ->
+    val z = { <!COMPONENT_FUNCTION_MISSING, COMPONENT_FUNCTION_MISSING, VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>(a: Int, b: String)<!> ->
         a checkType { _<Int>() }
         b checkType { _<String>() }
     }
diff --git a/compiler/testData/diagnostics/tests/functionLiterals/kt16016.fir.kt b/compiler/testData/diagnostics/tests/functionLiterals/kt16016.fir.kt
index 356cd30d48e..21414f0e215 100644
--- a/compiler/testData/diagnostics/tests/functionLiterals/kt16016.fir.kt
+++ b/compiler/testData/diagnostics/tests/functionLiterals/kt16016.fir.kt
@@ -1,6 +1,6 @@
 // !DIAGNOSTICS: -UNUSED_PARAMETER -UNUSED_VARIABLE
-val la = { a -> }
+val la = { <!VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>a<!> -> }
 val las = { a: Int -> }
 
-val larg = { a -> }(123)
-val twoarg = { a, b: String, c -> }(123, "asdf", 123)
\ No newline at end of file
+val larg = { <!VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>a<!> -> }(123)
+val twoarg = { <!VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>a<!>, b: String, <!VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>c<!> -> }(123, "asdf", 123)
diff --git a/compiler/testData/diagnostics/tests/inference/invokeLambdaAsFunction.fir.kt b/compiler/testData/diagnostics/tests/inference/invokeLambdaAsFunction.fir.kt
index 07047a5c1eb..2940be33e2a 100644
--- a/compiler/testData/diagnostics/tests/inference/invokeLambdaAsFunction.fir.kt
+++ b/compiler/testData/diagnostics/tests/inference/invokeLambdaAsFunction.fir.kt
@@ -1,7 +1,7 @@
-fun test1(i: Int) = { i ->
+fun test1(i: Int) = { <!VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>i<!> ->
     i
 }(i)
 
-fun test2() = { i -> i }<!NO_VALUE_FOR_PARAMETER!>()<!>
+fun test2() = { <!VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>i<!> -> i }<!NO_VALUE_FOR_PARAMETER!>()<!>
 
-fun test3() = { i -> i }(1)
+fun test3() = { <!VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>i<!> -> i }(1)
diff --git a/compiler/testData/diagnostics/tests/inference/kt12399.fir.kt b/compiler/testData/diagnostics/tests/inference/kt12399.fir.kt
index 216665dfc7e..acd4ad11ecb 100644
--- a/compiler/testData/diagnostics/tests/inference/kt12399.fir.kt
+++ b/compiler/testData/diagnostics/tests/inference/kt12399.fir.kt
@@ -1,3 +1,3 @@
 fun foo(a: Any) {
-    foo({ index -> } {  })
+    foo({ <!VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>index<!> -> } {  })
 }
\ No newline at end of file
diff --git a/compiler/testData/diagnostics/tests/inference/nonFunctionalExpectedTypeForLambdaArgument.fir.kt b/compiler/testData/diagnostics/tests/inference/nonFunctionalExpectedTypeForLambdaArgument.fir.kt
index 63780bd4239..09f86b373c6 100644
--- a/compiler/testData/diagnostics/tests/inference/nonFunctionalExpectedTypeForLambdaArgument.fir.kt
+++ b/compiler/testData/diagnostics/tests/inference/nonFunctionalExpectedTypeForLambdaArgument.fir.kt
@@ -32,5 +32,5 @@ fun testParamCall() {
 }
 
 fun testNoContext() {
-    { it -> it }
+    { <!VALUE_PARAMETER_WITH_NO_TYPE_ANNOTATION!>it<!> -> it }
 }
diff --git a/compiler/tests-common-new/tests-gen/org/jetbrains/kotlin/test/runners/DiagnosticTestGenerated.java b/compiler/tests-common-new/tests-gen/org/jetbrains/kotlin/test/runners/DiagnosticTestGenerated.java
index 02b1629fa12..7db4d46d1a7 100644
--- a/compiler/tests-common-new/tests-gen/org/jetbrains/kotlin/test/runners/DiagnosticTestGenerated.java
+++ b/compiler/tests-common-new/tests-gen/org/jetbrains/kotlin/test/runners/DiagnosticTestGenerated.java
@@ -195,6 +195,12 @@ public class DiagnosticTestGenerated extends AbstractDiagnosticTest {
             runTest("compiler/testData/diagnostics/tests/comparisonOfGenericInterfaceWithGenericClass.kt");
         }
 
+        @Test
+        @TestMetadata("compilerCrashParameterType.kt")
+        public void testCompilerCrashParameterType() throws Exception {
+            runTest("compiler/testData/diagnostics/tests/compilerCrashParameterType.kt");
+        }
+
         @Test
         @TestMetadata("Constants.kt")
         public void testConstants() throws Exception {